scholarly journals Thin $\mathrm{II}_{1}$ factors with no Cartan subalgebras

2019 ◽  
Vol 59 (4) ◽  
pp. 815-867
Author(s):  
Anna Sofie Krogager ◽  
Stefaan Vaes
Keyword(s):  
Cartan Subalgebras

scholarly journals Cartan subalgebras of operator ideals

2016 ◽  
Vol 65 (1) ◽  
pp. 1-37 ◽  
Author(s):  
Daniel Beltita ◽  
SASMITA PATNAIK ◽  
Gary Weiss
Keyword(s):  
Operator Ideals ◽  
Cartan Subalgebras

scholarly journals Cartan subalgebras of regular extensions of von Neumann algebras

1988 ◽  
Vol 45 (2) ◽  
pp. 249-274
Author(s):  
Colin E. Sutherland
Keyword(s):  
Cartan Subalgebra ◽  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
Regular Representation ◽  
Projective Representation ◽  
Von Neumann ◽  
Left Regular ◽  
Cartan Subalgebras ◽  
Inner Automorphisms ◽  
The Given

AbstractWe analyse the structure of a regular extension ℳ ⋊ γ, υQ of a von Neumann algebra ℳ by an action (modulo inner automorphisms) γ of a discrete group Q, and a nonabelian 2-cycle υ for γ, under the assumption that the “action” γ of Q is cocycle conjugate to an “action”, α which leaves globally invariant a cartan subalgebra of ℳ. we show that ℳ ⋊ γ, υQ is isomorphic with the algebra of the left regular projective representation of a certain discrete, non-principal groupoid ℜ V Q determined by the action of Q on the given cartan subalgebrs, where ℜ is the Takesaki relation associated to the pair (ℳ, ) we apply this description to give a decomposition of the regular representation of a group G into irreducibles, where G is a split extension of a type I group K by an abelian group Q, and work out the details of the author's earlier abstract plancherel theorem in the case when K is abelian.

scholarly journals Cartan Subalgebras of Leibniz n-Algebras

2009 ◽  
Vol 37 (6) ◽  
pp. 2080-2096 ◽  
Author(s):  
S. Albeverio ◽  
Sh. A. Ayupov ◽  
B. A. Omirov ◽  
R. M. Turdibaev
Keyword(s):  
Cartan Subalgebras

scholarly journals Cartan Subalgebras of Jordan Algebras

1966 ◽  
Vol 27 (2) ◽  
pp. 591-609 ◽  
Author(s):  
N. Jacobson
Keyword(s):  
Lie Algebra ◽  
Jordan Algebra ◽  
Cartan Subalgebra ◽  
Jordan Algebras ◽  
Classical Notion ◽  
Cartan Subalgebras ◽  
Definition Of

In this paper we shall give a definition of an analogue for Jordan algebras of the classical notion of a Cartan subalgebra of a Lie algebra. This is based on a notion of associator nilpotency of a Jordan algebra. A Jordan algebra is called associator nilpotent if there exists a positive (odd) integer M such that every associator of order M formed of elements of is 0 (§2).

Cartan Subalgebras of

2003 ◽  
Vol 46 (4) ◽  
pp. 597-616 ◽  
Author(s):  
Karl-Hermann Neeb ◽  
Ivan Penkov
Keyword(s):  
Finite Rank ◽  
Characteristic Zero ◽  
Cartan Subalgebra ◽  
Adjoint Representation ◽  
Linear Functionals ◽  
Maximal Subalgebra ◽  
Locally Finite ◽  
One Dimensional ◽  
Cartan Subalgebras ◽  
Locally Nilpotent

AbstractLet V be a vector space over a field of characteristic zero and V* be a space of linear functionals on V which separate the points of V. We consider V ⊗ V* as a Lie algebra of finite rank operators on V, and set (V, V*) := V ⊗ V*. We define a Cartan subalgebra of (V, V*) as the centralizer of a maximal subalgebra every element of which is semisimple, and then give the following description of all Cartan subalgebras of (V;V*) under the assumption that is algebraically closed. A subalgebra of (V, V*) is a Cartan subalgebra if and only if it equals for some one-dimensional subspaces Vj ⊆ V and (Vj)* ⊆ V* with (Vi)* (Vj) = δij and such that the spaces . We then discuss explicit constructions of subspaces Vj and (Vj)* as above. Our second main result claims that a Cartan subalgebra of (V, V*) can be described alternatively as a locally nilpotent self-normalizing subalgebra whose adjoint representation is locally finite, or as a subalgebra h which coincides with the maximal locally nilpotent h-submodule of (V, V*), and such that the adjoint representation of is locally finite.

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