The Experts below are selected from a list of 4782 Experts worldwide ranked by ideXlab platform
J Suzuki - One of the best experts on this subject based on the ideXlab platform.
-
anharmonic oscillators spectral determinant and Short Exact Sequence of
Journal of Physics A, 1999Co-Authors: J SuzukiAbstract:We prove one of the conjectures, raised by Dorey and Tateo (1998 Anharmonic oscillators, the thermodynamic Bethe ansatz, and nonlinear integral equations Preprint DTP-98/81, ITPA 98-41, (hep-th/9812211)) in the connection among the spectral determinant of anharmonic oscillator and vacuum eigenvalues of transfer matrices in field theory and statistical mechanics. The Exact Sequence of plays a fundamental role in the proof.
-
Anharmonic Oscillators, Spectral Determinant and Short Exact Sequence of affine U_q(sl_2)
Journal of Physics A: Mathematical and General, 1999Co-Authors: J SuzukiAbstract:We prove one of conjectures, raised by Dorey and Tateo in the connection among the spectral determinant of anharmonic oscillator and vacuum eigenvalues of transfer matrices in field theory and statistical mechanics. The Exact Sequence of $U_q(\hat{sl}_2)$ plays a fundamental role in the proof.
John Guaschi - One of the best experts on this subject based on the ideXlab platform.
-
Braid groups of non-orientable surfaces and the Fadell-Neuwirth Short Exact Sequence
Journal of Pure and Applied Algebra, 2010Co-Authors: Daciberg Gonçalves, John GuaschiAbstract:Let M be a compact, connected non-orientable surface without boundary and of genus g greater than or equal to 3. We investigate the pure braid groups P_n(M) of M, and in particular the possible splitting of the Fadell-Neuwirth Short Exact Sequence 1 --> P_m(M \ {x_1,...,x_n}) --> P_{n+m}(M) --> P_n(M) --> 1, where m,n are positive integers, and the homomorphism p*:P_{n+m}(M) --> P_n(M) corresponds geometrically to forgetting the last m strings. This problem is equivalent to that of the existence of a section for the associated fibration p:F_{n+m}(M)} --> F_n(M) of configuration spaces, defined by p((x_1,...,x_n,..., x_{n+m}))= (x_1, ..., x_n). We show that p and p* admit a section if and only if n=1. Together with previous results, this completes the resolution of the splitting problem for surfaces pure braid groups.
-
braid groups of non orientable surfaces and the fadell neuwirth Short Exact Sequence
Journal of Pure and Applied Algebra, 2010Co-Authors: Daciberg Lima Gonçalves, John GuaschiAbstract:Abstract Let M be a compact, connected non-orientable surface without boundary and of genus g ⩾ 3 . We investigate the pure braid groups P n ( M ) of M , and in particular the possible splitting of the Fadell–Neuwirth Short Exact Sequence 1 ⟶ P m ( M ∖ { x 1 , … , x n } ) ↪ P n + m ( M ) ⟶ p ∗ P n ( M ) ⟶ 1 , where m , n ⩾ 1 , and p ∗ is the homomorphism which corresponds geometrically to forgetting the last m strings. This problem is equivalent to that of the existence of a section for the associated fibration p : F n + m ( M ) ⟶ F n ( M ) of configuration spaces, defined by p ( ( x 1 , … , x n , x n + 1 , … , x n + m ) ) = ( x 1 , … , x n ) . We show that p and p ∗ admit a section if and only if n = 1 . Together with previous results, this completes the resolution of the splitting problem for surface pure braid groups.
-
Braid groups of non-orientable surfaces and the Fadell–Neuwirth Short Exact Sequence
Journal of Pure and Applied Algebra, 2010Co-Authors: Daciberg Lima Gonçalves, John GuaschiAbstract:Abstract Let M be a compact, connected non-orientable surface without boundary and of genus g ⩾ 3 . We investigate the pure braid groups P n ( M ) of M , and in particular the possible splitting of the Fadell–Neuwirth Short Exact Sequence 1 ⟶ P m ( M ∖ { x 1 , … , x n } ) ↪ P n + m ( M ) ⟶ p ∗ P n ( M ) ⟶ 1 , where m , n ⩾ 1 , and p ∗ is the homomorphism which corresponds geometrically to forgetting the last m strings. This problem is equivalent to that of the existence of a section for the associated fibration p : F n + m ( M ) ⟶ F n ( M ) of configuration spaces, defined by p ( ( x 1 , … , x n , x n + 1 , … , x n + m ) ) = ( x 1 , … , x n ) . We show that p and p ∗ admit a section if and only if n = 1 . Together with previous results, this completes the resolution of the splitting problem for surface pure braid groups.
-
The braid groups of the projective plane and the Fadell-Neuwirth Short Exact Sequence
Geometriae Dedicata, 2007Co-Authors: Daciberg Lima Gonçalves, John GuaschiAbstract:We study the pure braid groups $P_n(RP^2)$ of the real projective plane $RP^2$, and in particular the possible splitting of the Fadell-Neuwirth Short Exact Sequence $1 \to P_m(RP^2 {x_1,...,x_n} \to P_{n+m}(RP^2) \stackrel{p_{\ast}}{\to} P_n(RP^2) \to 1$, where $n\geq 2$ and $m\geq 1$, and $p_{\ast}$ is the homomorphism which corresponds geometrically to forgetting the last $m$ strings. This problem is equivalent to that of the existence of a section for the associated fibration $p: F_{n+m}(RP^2) \to F_n(RP^2)$ of configuration spaces. Van Buskirk proved in 1966 that $p$ and $p_{\ast}$ admit a section if $n=2$ and $m=1$. Our main result in this paper is to prove that there is no section if $n\geq 3$. As a corollary, it follows that $n=2$ and $m=1$ are the only values for which a section exists. As part of the proof, we derive a presentation of $P_n(RP^2)$: this appears to be the first time that such a presentation has been given in the literature.
-
THE BRAID GROUP $B_{n,m}(\mathbb{S}^{2})$ AND A GENERALISATION OF THE FADELL–NEUWIRTH Short Exact Sequence
Journal of Knot Theory and Its Ramifications, 2005Co-Authors: Daciberg Lima Gonçalves, John GuaschiAbstract:Let m,n ∈ ℕ. We define to be the set of (n+m)-braids of the sphere whose associated permutation lies in the subgroup Sn × Sm of the symmetric group Sn+m on n+m letters. In a previous paper [13], we showed that if n ≥ 3, then there exists the following generalisation of the Fadell–Neuwirth Short Exact Sequence: where is the group homomorphism (defined for all n ∈ ℕ) given geometrically by forgetting the last m strings. In this paper we study the splitting of this Short Exact Sequence, as well as the existence of a cross-section for the fibration of the quotients of the corresponding configuration spaces. Our main results are as follows: if n = 1 (respectively, n = 2) then the homomorphism p* and the fibration p admit (respectively, do not admit) a section. If n = 3, then p* and p admit a section if and only if m ≡ 0,2 (mod 3). If n ≥ 4, we show that if p* and p admit a section then m ≡ e1(n - 1)(n - 2) - e2n(n - 2) (mod n(n - 1)(n - 2)), where e1,e2 ∈ {0,1}. Finally, we show that is generated by two of its torsion elements.
Hossein Mohammadzadeh Saany - One of the best experts on this subject based on the ideXlab platform.
-
Preservation of Rees Exact Sequences
Mathematica Slovaca, 2019Co-Authors: Morteza Jafari, Akbar Golchin, Hossein Mohammadzadeh SaanyAbstract:Abstract Yuqun Chen and K. P. Shum in [Rees Short Exact Sequence of S-systems, Semigroup Forum 65 (2002), 141–148] introduced Rees Short Exact Sequence of acts and considered conditions under which a Rees Short Exact Sequence of acts is left and right split, respectively. To our knowledge, conditions under which the induced Sequences by functors Hom(RLS, –), Hom(–, RLS) and AS ⊗ S– (where R, S are monoids) are Exact, are unknown. This article addresses these conditions. Results are different from that of modules.
-
Rees Short Exact Sequence and flatness properties
Semigroup Forum, 2018Co-Authors: Morteza Jafari, Akbar Golchin, Hossein Mohammadzadeh SaanyAbstract:Chen and Shum (Semigroup Forum 65:141–148, 2002) introduced Rees Short Exact Sequence of acts over monoids and considered conditions under which a Rees Short Exact Sequence of acts is left and right split, respectively. In this paper we investigate conditions under which flatness properties of right acts A and C in the Rees Short Exact Sequence \( 0 \longrightarrow A {\mathop {\longrightarrow }\limits ^{f}} B {\mathop {\longrightarrow }\limits ^{g}} C \longrightarrow 0 \) can be transferred to B.
Kar-ping Shum - One of the best experts on this subject based on the ideXlab platform.
-
Rees Short Exact Sequences of S-systems
Semigroup Forum, 2002Co-Authors: Yuqun Chen, Kar-ping ShumAbstract:In this article, the conditions for a Rees Short Exact Sequence of S -systems to be left and right split, respectively, are given. We note that this result differs from the well known result of an Exact Sequence of modules that is split.
Daciberg Lima Gonçalves - One of the best experts on this subject based on the ideXlab platform.
-
braid groups of non orientable surfaces and the fadell neuwirth Short Exact Sequence
Journal of Pure and Applied Algebra, 2010Co-Authors: Daciberg Lima Gonçalves, John GuaschiAbstract:Abstract Let M be a compact, connected non-orientable surface without boundary and of genus g ⩾ 3 . We investigate the pure braid groups P n ( M ) of M , and in particular the possible splitting of the Fadell–Neuwirth Short Exact Sequence 1 ⟶ P m ( M ∖ { x 1 , … , x n } ) ↪ P n + m ( M ) ⟶ p ∗ P n ( M ) ⟶ 1 , where m , n ⩾ 1 , and p ∗ is the homomorphism which corresponds geometrically to forgetting the last m strings. This problem is equivalent to that of the existence of a section for the associated fibration p : F n + m ( M ) ⟶ F n ( M ) of configuration spaces, defined by p ( ( x 1 , … , x n , x n + 1 , … , x n + m ) ) = ( x 1 , … , x n ) . We show that p and p ∗ admit a section if and only if n = 1 . Together with previous results, this completes the resolution of the splitting problem for surface pure braid groups.
-
Braid groups of non-orientable surfaces and the Fadell–Neuwirth Short Exact Sequence
Journal of Pure and Applied Algebra, 2010Co-Authors: Daciberg Lima Gonçalves, John GuaschiAbstract:Abstract Let M be a compact, connected non-orientable surface without boundary and of genus g ⩾ 3 . We investigate the pure braid groups P n ( M ) of M , and in particular the possible splitting of the Fadell–Neuwirth Short Exact Sequence 1 ⟶ P m ( M ∖ { x 1 , … , x n } ) ↪ P n + m ( M ) ⟶ p ∗ P n ( M ) ⟶ 1 , where m , n ⩾ 1 , and p ∗ is the homomorphism which corresponds geometrically to forgetting the last m strings. This problem is equivalent to that of the existence of a section for the associated fibration p : F n + m ( M ) ⟶ F n ( M ) of configuration spaces, defined by p ( ( x 1 , … , x n , x n + 1 , … , x n + m ) ) = ( x 1 , … , x n ) . We show that p and p ∗ admit a section if and only if n = 1 . Together with previous results, this completes the resolution of the splitting problem for surface pure braid groups.
-
A note on generalized equivariant homotopy groups
arXiv: Algebraic Topology, 2007Co-Authors: Marek Golasiński, Daciberg Lima Gonçalves, Peter WongAbstract:In this paper, we generalize the equivariant homotopy groups or equivalently the Rhodes groups. We establish a Short Exact Sequence relating the generalized Rhodes groups and the generalized Fox homotopy groups and we introduce $\Gamma$-Rhodes groups, where $\Gamma$ admits a certain co-grouplike structure. Evaluation subgroups of $\Gamma$-Rhodes groups are discussed.
-
The braid groups of the projective plane and the Fadell-Neuwirth Short Exact Sequence
Geometriae Dedicata, 2007Co-Authors: Daciberg Lima Gonçalves, John GuaschiAbstract:We study the pure braid groups $P_n(RP^2)$ of the real projective plane $RP^2$, and in particular the possible splitting of the Fadell-Neuwirth Short Exact Sequence $1 \to P_m(RP^2 {x_1,...,x_n} \to P_{n+m}(RP^2) \stackrel{p_{\ast}}{\to} P_n(RP^2) \to 1$, where $n\geq 2$ and $m\geq 1$, and $p_{\ast}$ is the homomorphism which corresponds geometrically to forgetting the last $m$ strings. This problem is equivalent to that of the existence of a section for the associated fibration $p: F_{n+m}(RP^2) \to F_n(RP^2)$ of configuration spaces. Van Buskirk proved in 1966 that $p$ and $p_{\ast}$ admit a section if $n=2$ and $m=1$. Our main result in this paper is to prove that there is no section if $n\geq 3$. As a corollary, it follows that $n=2$ and $m=1$ are the only values for which a section exists. As part of the proof, we derive a presentation of $P_n(RP^2)$: this appears to be the first time that such a presentation has been given in the literature.
-
THE BRAID GROUP $B_{n,m}(\mathbb{S}^{2})$ AND A GENERALISATION OF THE FADELL–NEUWIRTH Short Exact Sequence
Journal of Knot Theory and Its Ramifications, 2005Co-Authors: Daciberg Lima Gonçalves, John GuaschiAbstract:Let m,n ∈ ℕ. We define to be the set of (n+m)-braids of the sphere whose associated permutation lies in the subgroup Sn × Sm of the symmetric group Sn+m on n+m letters. In a previous paper [13], we showed that if n ≥ 3, then there exists the following generalisation of the Fadell–Neuwirth Short Exact Sequence: where is the group homomorphism (defined for all n ∈ ℕ) given geometrically by forgetting the last m strings. In this paper we study the splitting of this Short Exact Sequence, as well as the existence of a cross-section for the fibration of the quotients of the corresponding configuration spaces. Our main results are as follows: if n = 1 (respectively, n = 2) then the homomorphism p* and the fibration p admit (respectively, do not admit) a section. If n = 3, then p* and p admit a section if and only if m ≡ 0,2 (mod 3). If n ≥ 4, we show that if p* and p admit a section then m ≡ e1(n - 1)(n - 2) - e2n(n - 2) (mod n(n - 1)(n - 2)), where e1,e2 ∈ {0,1}. Finally, we show that is generated by two of its torsion elements.