In this paper, we determine the isomorphism classes of the central simple Poisson algebras introduced earlier by the second author. The Lie algebra structures of these Poisson algebras are in general not finitely-graded.

A self-dual algebra is an associative or Lie algebra A together with an A bimodule isomorphism A → A∨op, where A∨ = Homk(A, k), the dual bimodule to A (considered as an A bimodule), and A∨op is the the same underlying k module as A∨ but is an A bimodule whose left operation by an element a ∈ A is the same as the right operation by a on A∨, and similarly with left and right interchanged. This in...

There are eighteen isomorphism types of finite relation algebras with eight or fewer elements, and all of them are representable. We determine all the cardinalities of sets on which these algebras have representations.

A theorem is presented on existence and uniqueness up to the topological *-isomorphism of universal locally C*-algebra for an arbitrary locally JB-algebra. The abstract Banach associative symmetrical *-algebras over C, so called C*algebras, were introduces first by Gelfand and Naimark in []. In the present time the theory of C*-algebras become a vast portion of Functional Analysis having connec...

Assume A is a Fréchet algebra equipped with a smooth isometric action of a vector group V , and consider Rieffel’s deformation AJ of A. We construct an explicit isomorphism between the smooth crossed products V n AJ and V n A. When combined with the Elliott-Natsume-Nest isomorphism, this immediately implies that the periodic cyclic cohomology is invariant under deformation. Specializing to the ...

The paper continues the study of differential Banach *algebras AS and FS of operators associated with symmetric operators S on Hilbert spaces H. The algebra AS is the domain of the largest *-derivation δS of B(H) implemented by S and the algebra FS is the closure of the set of all finite rank operators in AS with respect to the norm ‖A‖ = ‖A‖+‖δS(A)‖. When S is selfadjoint, FS is the domain of ...