The Experts below are selected from a list of 34107 Experts worldwide ranked by ideXlab platform
Jesse Peterson - One of the best experts on this subject based on the ideXlab platform.
-
l 2 rigidity in von neumann algebras
Inventiones Mathematicae, 2009Co-Authors: Jesse PetersonAbstract:We introduce the notion of L2-rigidity for von Neumann algebras, a generalization of property (T) which can be viewed as an analogue for the vanishing of 1-cohomology into the left Regular Representation of a group. We show that L2-rigidity passes to normalizers and is satisfied by nonamenable II1 factors which are non-prime, have property Γ, or are weakly rigid. As a consequence we obtain that if M is a free product of diffuse von Neumann algebras, or if M=LΓ where Γ is a finitely generated group with β1(2)(Γ)>0, then any nonamenable Regular subfactor of M is prime and does not have properties Γ or (T). In particular this gives a new approach for showing solidity for a free group factor thus recovering a well known recent result of N. Ozawa.
-
l 2 rigidity in von neumann algebras
arXiv: Operator Algebras, 2006Co-Authors: Jesse PetersonAbstract:We introduce the notion of L^2-rigidity for von Neumann algebras, a generalization of property (T) which can be viewed as an analogue for the vanishing of 1-cohomology into the left Regular Representation of a group. We show that L^2-rigidity passes to normalizers and is satisfied by nonamenable II_1 factors which are non-prime, have property $\Gamma$, or are weakly rigid. As a consequence we obtain that if $M$ is a free product of diffuse von Neumann algebras, or if $M = L\Gamma$ where $\Gamma$ is a finitely generated group with $b_1^{(2)}(\Gamma) > 0$, then any nonamenable Regular subfactor of $M$ is prime and does not have properties $\Gamma$ or (T). In particular this gives a new approach for showing primeness of all nonamenable subfactors of a free group factor thus recovering a well known recent result of N. Ozawa.
J T Sobczyk - One of the best experts on this subject based on the ideXlab platform.
-
left Regular Representation and contraction of sl q 2 to e q 2
Letters in Mathematical Physics, 1994Co-Authors: Ludwik Dabrowski, J T SobczykAbstract:The left Regular Representation of the quantum algebras sl q (2) and e q (2) are discussed and shown to be related by contraction. The reducibility is studied andq-difference intertwining operators are constructed.
V Losert - One of the best experts on this subject based on the ideXlab platform.
-
the c algebra generated by operators with compact support on a locally compact group
Journal of Functional Analysis, 1993Co-Authors: V LosertAbstract:Abstract Let G be a locally compact group and VN(G) be the von Neumann algebra generated by the left Regular Representation of G. Let UCB(Ĝ) denote the C*-subalgebra generated by operators in VN(G) with compact support. When G is abelian, UCB(Ĝ) corresponds to the space of bounded uniformly continuous functions on the dual group Ĝ of G. In this paper we prove among other things that for a large class of locally compact groups which include the Heisenberg group, the "ax + b" group and the motion group, the centre of the Banach algebra UCB(Ĝ)* is the Fourier Stieltjes algebra B(G).
Pablo Spiga - One of the best experts on this subject based on the ideXlab platform.
-
a classification of the m graphical Regular Representation of finite groups
arXiv: Combinatorics, 2019Co-Authors: Yanquan Feng, Pablo SpigaAbstract:In this paper we extend the classical notion of digraphical and graphical Regular Representation of a group and we classify, by means of an explicit description, the finite groups satisfying this generalization. A graph or digraph is called Regular if each vertex has the same valency, or, the same out-valency and the same in-valency, respectively. An m-(di)graphical Regular Representation (respectively, m-GRR and m-DRR, for short) of a group G is a Regular (di)graph whose automorphism group is isomorphic to G and acts semiRegularly on the vertex set with m orbits. When m=1, this definition agrees with the classical notion of GRR and DRR. Finite groups admitting a 1-DRR were classified by Babai in 1980, and the analogue classification of finite groups admitting a 1-GRR was completed by Godsil in 1981. Pivoting on these two results in this paper we classify finite groups admitting an m-GRR or an m-DRR, for arbitrary positive integers m. For instance, we prove that every non-identity finite group admits an m-GRR, for every m>4.
-
classification of finite groups that admit an oriented Regular Representation
Bulletin of The London Mathematical Society, 2018Co-Authors: Joy Morris, Pablo SpigaAbstract:This is the third, and last, of a series of papers dealing with oriented Regular Representations. Here we complete the classification of finite groups that admit an oriented Regular Representation (or ORR for short), and give a complete answer to a 1980 question of Laszlo Babai: "Which [finite] groups admit an oriented graph as a DRR?" It is easy to see and well-understood that generalised dihedral groups do not admit ORRs. We prove that, with 11 small exceptions (having orders ranging from 8 to 64), every finite group that is not generalised dihedral has an ORR.
-
finite groups admitting an oriented Regular Representation
Journal of Combinatorial Theory Series A, 2018Co-Authors: Pablo SpigaAbstract:Abstract In this paper, we investigate finite groups admitting an oriented Regular Representation and we give a partial answer to a 1980 question of Lazslo Babai: “Which [finite] groups admit an oriented graph as a DRR?” It is easy to see and well-understood that generalised dihedral groups do not admit ORRs. We prove that, apart from C 3 2 and C 3 × C 2 3 , every finite group, which is neither a generalised dihedral group nor a 2-group, has an ORR. In particular, the classification of the finite groups admitting an ORR is reduced to the class of 2-groups. We also give strong structural conditions on finite 2-groups not admitting an ORR. Finally, based on these results and on some extensive computer computations, we state a conjecture aiming to give a complete classification of the finite groups admitting an ORR.
-
every finite non solvable group admits an oriented Regular Representation
Journal of Combinatorial Theory Series B, 2017Co-Authors: Joy Morris, Pablo SpigaAbstract:Abstract In this paper we give a partial answer to a 1980 question of Lazslo Babai: “Which [finite] groups admit an oriented graph as a DRR?” That is, which finite groups admit an oriented Regular Representation (ORR)? We show that every finite non-solvable group admits an ORR, and provide a tool that may prove useful in showing that some families of finite solvable groups admit ORRs. We also completely characterize all finite groups that can be generated by at most three elements, according to whether or not they admit ORRs.
Ludwik Dabrowski - One of the best experts on this subject based on the ideXlab platform.
-
left Regular Representation and contraction of sl q 2 to e q 2
Letters in Mathematical Physics, 1994Co-Authors: Ludwik Dabrowski, J T SobczykAbstract:The left Regular Representation of the quantum algebras sl q (2) and e q (2) are discussed and shown to be related by contraction. The reducibility is studied andq-difference intertwining operators are constructed.
