The Experts below are selected from a list of 15939 Experts worldwide ranked by ideXlab platform
Paul S Pedersen - One of the best experts on this subject based on the ideXlab platform.
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cauchy s integral theorem on a finitely generated real commutative and Associative Algebra
Advances in Mathematics, 1997Co-Authors: Paul S PedersenAbstract:LetR[α]=R[α1, α2, …, αn] (whereα1=1) be a real, unitary, finitely generated, commutative, and Associative Algebra. We consider functionsf(z)=f(∑ni=1 xiαi) which mapR[α]n={∑ni=1 aiαi | 1⩽i⩽n,ai∈R} intoR[α]=finite dimensional subspaces of {∑k∈Nn0 bkαk | bk∈R,k=(k1, …, kn)∈Nn0} whereN0={0, 1, 2, …}. We impose a total order on an algorithmically defined basisBforR[α]. The resulting Algebra and ordered basis will be written as (R[α], <). We then use this basis to define a norm ‖·‖ on (R[α], <). Continuous functions, differentiable functions, and the concept of Riemann integration will then be defined and discussed in this new setting. We then show that ∫γ f(z) dz=0 whenf(z) is a continuous and differentiable function defined in a simply connected regionG⊂R[α]n⊂(R[α], <) containing the closed pathγ.
Franklin E Schroeck - One of the best experts on this subject based on the ideXlab platform.
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the poincare group in a demisemidirect product with a non Associative Algebra with representations that include particles and quarks ii
International Journal of Theoretical Physics, 2009Co-Authors: Franklin E SchroeckAbstract:The quarks and particles’ mass and mass/spin relations are provided with coordinates in configuration space and/or momentum space by means of the marriage of ordinary Poincare group representations with a non-Associative Algebra made through a demisemidirect product, in the notation of Leibniz Algebras. Thus, we circumvent the restriction that the Poincare group cannot be extended to a larger group by any means (including the (semi)direct product) to get even the mass relations. Finally, we will discuss a connection between the phase space representations of the Poincare group and the phase space representations of the associated Leibniz Algebra.
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the poincaŕ group in a demisemidirect product with a non Associative Algebra with representations that include particles and quarks
GEOMETRIC METHODS IN PHYSICS, 2008Co-Authors: Franklin E SchroeckAbstract:The quarks have always been a puzzle, as have the particles’ mass and mass/spin relations as they seemed to have no coordinates in configuration space and/or momentum space. The solution to this seems to lie in the marriage of ordinary Poincare group representations with a non‐Associative Algebra made through a demisemidirect product. Then, the work of G. Dixon applies; so, we may obtain all the relations between masses, mass and spin, and the attribution of position and momentum to quarks—this in spite of the old restriction that the Poincare group cannot be extended to a larger group by any means (including the (semi)direct product) to get even the mass relations. Finally, we will briefly discuss a possible connection between the phase space representations of the Poincare group and the phase space representations of the object we will obtain. This will take us into Leibniz (co)homology.
Apurba Das - One of the best experts on this subject based on the ideXlab platform.
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Noncommutative differential calculus on (co)homology of hom-Associative Algebras
Communications in Algebra, 2021Co-Authors: Apurba DasAbstract:A hom-Associative Algebra is an Algebra whose associativity is twisted by an Algebra homomorphism. It was previously shown by the author that the Hochschild cohomology of a hom-Associative Algebra ...
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Noncommutative differential calculus on (co)homology of hom-Associative Algebras
arXiv: Rings and Algebras, 2020Co-Authors: Apurba DasAbstract:A hom-Associative Algebra is an Algebra whose associativity is twisted by an Algebra homomorphism. It was previously shown by the author that the Hochschild cohomology of a hom-Associative Algebra $A$ carries a Gerstenhaber structure. In this short paper, we show that this Gerstenhaber structure together with certain operations on the Hochschild homology of $A$ makes a noncommutative differential calculus. As an application, we obtain a Batalin-Vilkovisky Algebra structure on the Hochschild cohomology of a regular unital symmetric hom-Associative Algebra.
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Gerstenhaber Algebra structure on the cohomology of a hom-Associative Algebra
Proceedings - Mathematical Sciences, 2020Co-Authors: Apurba DasAbstract:A hom-Associative Algebra is an Algebra whose associativity is twisted by an Algebra homomorphism. In this paper, we define a cup product on the cohomology of a hom-Associative Algebra. A direct verification shows that this cup product together with the degree $$-1$$ graded Lie bracket (which controls the deformation of the hom-Associative Algebra structure) on the cohomology makes it a Gerstenhaber Algebra.
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Gerstenhaber Algebra structure on the cohomology of a hom-Associative Algebra
arXiv: Rings and Algebras, 2018Co-Authors: Apurba DasAbstract:A hom-Associative Algebra is an Algebra whose associativity is twisted by an Algebra homomorphism. In this paper, we define a cup product on the cohomology of a hom-Associative Algebra. We show that the cup product together with the degree $-1$ graded Lie bracket (which controls the deformation of the hom-Associative Algebra structure) on the cohomology forms a Gerstenhaber Algebra. This generalizes a classical fact that the Hochschild cohomology of an Associative Algebra carries a Gerstenhaber Algebra structure.
Luca Vitagliano - One of the best experts on this subject based on the ideXlab platform.
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on the strong homotopy Associative Algebra of a foliation
Communications in Contemporary Mathematics, 2015Co-Authors: Luca VitaglianoAbstract:An involutive distribution C on a smooth manifold M is a Lie-algebroid acting on sections of the normal bundle TM/C. It is known that the Chevalley–Eilenberg complex associated to this representation of C possesses the structure 𝕏 of a strong homotopy Lie–Rinehart Algebra. It is natural to interpret 𝕏 as the (derived) Lie–Rinehart Algebra of vector fields on the space P of integral manifolds of C. In this paper, we show that 𝕏 is embedded in an A∞-Algebra 𝔻 of (normal) differential operators. It is natural to interpret 𝔻 as the (derived) Associative Algebra of differential operators on P. Finally, we speculate about the interpretation of 𝔻 as the universal enveloping strong homotopy Algebra of 𝕏.
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on the strong homotopy Associative Algebra of a foliation
arXiv: Differential Geometry, 2012Co-Authors: Luca VitaglianoAbstract:An involutive distribution $C$ on a smooth manifold $M$ is a Lie-algebroid acting on sections of the normal bundle $TM/C$. It is known that the Chevalley-Eilenberg complex associated to this representation of $C$ possesses the structure $\mathbb{X}$ of a strong homotopy Lie-Rinehart Algebra. It is natural to interpret $\mathbb{X}$ as the (derived) Lie-Rinehart Algebra of vector fields on the space $\mathbb{P}$ of integral manifolds of $C$. In this paper, I show that $\mathbb{X}$ is embedded in a strong homotopy Associative Algebra $\mathbb{D}$ of (normal) differential operators. It is natural to interpret $\mathbb{D}$ as the (derived) Associative Algebra of differential operators on $\mathbb{P}$. Finally, I speculate about the interpretation of $\mathbb{D}$ as the universal enveloping strong homotopy Algebra of $\mathbb{X}$.
A. Berzins - One of the best experts on this subject based on the ideXlab platform.
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the group of automorphisms of the semigroup of endomorphisms of free commutative and free Associative Algebras
International Journal of Algebra and Computation, 2007Co-Authors: A. BerzinsAbstract:Let W(X) be a free commutative or a free Associative Algebra. The group of automorphisms of the semigroup End(W(X)) is studied.
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AUTOMORPHISMS OF THE ENDOMORPHISM SEMIGROUP OF A FREE Associative Algebra
International Journal of Algebra and Computation, 2007Co-Authors: Alexei Belov-kanel, A. Berzins, Ruvim LipyanskiAbstract:Let be the variety of Associative Algebras over a field K and A = K 〈x1,…, xn〉 be a free Associative Algebra in the variety freely generated by a set X = {x1,…, xn}, End A the semigroup of endomorphisms of A, and Aut End A the group of automorphisms of the semigroup End A. We prove that the group Aut End A is generated by semi-inner and mirror automorphisms of End A. A similar result is obtained for the automorphism group Aut , where is the subcategory of finitely generated free Algebras of the variety . The later result solves Problem 3.9 formulated in [17].
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the group of automorphisms of semigroup of endomorphisms of free commutative and free Associative Algebras
arXiv: Algebraic Geometry, 2005Co-Authors: A. BerzinsAbstract:In this paper are described the groups of automorphisms of semigroup End(W(X)), where W(X) is free commutative or free Associative Algebra.
