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Quantum Boolean Algebras     Quantum Boolean Algebras  math       2010/11/24
We introduce quantum Boolean algebras which are the analogue of the Weyl algebras for Boolean affine spaces. We study quantum Boolean algebras from the logical and set theoretical viewpoints.
A topological space TO(S) of total orderings on any given set S is introduced and it is shown that TO(S) is compact if S is countable. The set NO(N) of all normal orderings of the nth Weyl algebra W ...
We consider the bound quiver algebras whose ordinary quiver is that of a canonical algebra. We determine which of those algebras are hereditary, tilted, quasitilted, weakly shod or laura algebras.
We investigate the lowest weight representations of the super Schrodinger algebras introduced by Duval and Horvathy. This is done by the same procedure as the semisimple Lie algebras. Namely, all sin...
We give a complete answer to the questions of factoriality, type classification and fullness for arbitrary free product von Neumann algebras
Transformation of operator algebras under Hopf algebra twist is studied. It is shown that that adjoint module algebras are stable under the twist. Applications to vector fields on non-commutative spac...
The goal of this paper is to present some results and (more importantly) state a number of conjectures suggesting that the representation theory of symplectic reflection algebras for wreath products c...
LetAbe a unital algebra equippedwith an involution (·)†, and suppose that the multiplicative set S ⊆ A generated by the elements of the form 1 + a†a satisfies the Ore condition.
In prime characteristic we introduce the notion of restricted pre-Lie algebra. We prove in the pre-Lie context the analogue to Jacobson's theorem for restricted Lie algebras. In particular, we prove t...
Let $C^*(E)$ be the graph $C^*$-algebra associated to a graph E and let J be a gauge invariant ideal in $C^*(E)$. We compute the cyclic six-term exact sequence in $K$-theory of the associated extensio...
We show that if $k$ is a countable field, then there exists a finitely generated, infinite-dimensional, primitive algebraic $k$-algebra $A$ whose Gelfand-Kirillov dimension is at most six. In additio...
This article gives a local answer to the coquecigrue problem. Hereby we mean the problem, formulated by J-L. Loday in \cite{LodayEns}, is that of finding a generalization of the Lie's third theorem fo...
We give sufficient conditions for the descent construction to be the universal central extension of a twisted form of a split simple Lie algebra over a ring. In particular, the universal central exten...
We present a program that allows for the computation of tensor products of irreducible representations of Lie algebras A-G based on the explicit construction of weight states. This straightforward ap...
We give a complete point-symmetry classification of all third-order evolution equations of the form $u_t=F(t,x,u,u_x, u_{xx})u_{xxx}+G(t,x,u,u_x, u_{xx})$ which admit semi-simple symmetry algebras and...

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