A concept of orientation is relevant for the passage from Jordan structure to associative structure in operator algebras. The research reported in this paper bridges the approach of Connes for von Neumann algebras and ourselves for C*-algebras in a general theory of orientation that is of geometric nature and is related to dynamics.

We construct an explicit set of generators for the finite W -algebras associated to nilpotent matrices in the symplectic or orthogonal Lie algebras whose Jordan blocks are all of the same size. We use these generators to show that such finite W -algebras are quotients of twisted Yangians.

The aim of this work is to introduce and study the notions Hom-pre-Jordan algebra Hom-J-dendriform which generalize Hom-Jordan algebras. algebras are regarded as underlying algebraic structures behind Rota-Baxter operators O-operators introduced in paper. also analogues Hom-pre-Lie for anti-commutator a left multiplication operator gives representation algebra. On other hand, analogue Hom-dendr...

We investigate 2-local ∗-automorphisms, 2-local ∗-antiautomorphisms, and 2-local Jordan ∗-derivations on certain algebras with involution.

A generalization of the Jordan–Schwinger map: classical version and its q–deformation. Abstract For all three–dimensional Lie algebras the construction of generators in terms of functions on 4-dimensional real phase space is given with a realization of the Lie product in terms of Poisson brackets. This is the classical Jordan–Schwinger map which is also given for the deformed algebras SL q (2, ...

We prove that a Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra is a ring homomorphism. Using a signum effectively, we can give a simple proof of the Hyers-Ulam-Rassias stability of a Jordan homomorphism between Banach algebras. As a direct corollary, we show that to each approximate Jordan homomorphism f from a Banach algebra into a semisimple commutative...

Synaptic algebras, introduced by D. Foulis, generalize different algebraic structures used so far as mathematical models of quantum mechanics: the traditional Hilbert space approach, order unit spaces, Jordan effect MV-algebras, orthomodular lattices. We study sharp and fuzzy observables on two special classes synaptic algebras: called generalized Hermitian algebras which are Banach duals. Rela...

1 Background and Motivation We start with an example of affine Kac-Moody algebras and the Virasoro algebra. In this talk, F will be a field with characteristic 0, and all the vector spaces are assumed over F. Denote by Z the ring of integers and by N the set of nonnegative integers. Let 2 ≤ n ∈ N. Set sl(n,F) = {A ∈ Mn×n(F) | tr A = 0}, (1.1) 〈A,B〉 = tr AB for A,B ∈ sl(n,F), (1.2) where Mn×n(F)...

This paper is devoted to the generalization of construction a Jordan algebra Lie and known theorems on local finite-dimensionality PI-algebras with an algebraic adjoint representation Mal’tsev algebras.