Jordan C*-algebras go back to Kaplansky, see [20]. Let J be a complex Banach Jordan algebra, that is, a complex Banach space with commutative bilinear product x◦y satisfying x◦(x2◦y) = x2◦(x◦y) as well as ||x◦y|| ≤ ||x||·||y||, Bounded symmetric domains and generalized operator algebras 51 and suppose that on J is given a (conjugate linear) isometric algebra involution x 7→ x∗. Then J is called...

A classical theorem of Burnside asserts that if X is a faithful complex character for the finite group G, then every irreducible character of G is a constituent of some power Xn of X . Fifty years after this appeared, Steinberg generalized it to a result on semigroup algebras K[G] with K an arbitrary field and with G a semigroup, finite or infinite. Five years later, Rieffel showed that the the...

We introduce a dual notion of the Poisson algebra, called transposed by exchanging roles two binary operations in Leibniz rule defining algebra. The algebra shares common properties and arises naturally from Novikov-Poisson taking commutator Lie Novikov Consequently, classic construction commutative with commuting derivations similarly applies to More broadly, captures algebraic structures when...

We study the Poisson (co)homology of the algebra of truncated polynomials in two variables viewed as the semi-classical limit of a quantum complete intersection studied by Bergh and Erdmann. We show in particular that the Poisson cohomology ring of such a Poisson algebra is isomorphic to the Hochschild cohomology ring of the corresponding quantum complete intersection.

2 Vertex algebras, associative filtered algebras and Poisson algebras 1 2.1 Vertex algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2.2 The enveloping algebra U(V ) of V . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 The Poisson algebra Ps(V ) of V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 Poisson algebras and modules ...

Let A1 = K〈X,Y | [Y,X] = 1〉 be the (first) Weyl algebra over a field K of characteristic zero. It is known that the set of eigenvalues of the inner derivation ad(Y X) of A1 is Z. Let A1 → A1, X 7→ x, Y 7→ y, be a K-algebra homomorphism, i.e. [y, x] = 1. It is proved that the set of eigenvalues of the inner derivation ad(yx) of theWeyl algebra A1 is Z and the eigenvector algebra of ad(yx) is K〈x...

We generalize the notion of the rank-generating function of a graded poset. Namely, by enumerating different chains in a poset, we can assign a quasi-symmetric function to the poset. This map is a Hopf algebra homomorphism between the reduced incidence Hopf algebra of posets and the Hopf algebra of quasi-symmetric functions. This work implies that the zeta polynomial of a poset may be viewed in...

We investigate how the matrix representation of SU(N) algebra approaches that of the Poisson algebra in the large N limit. In the adjoint representation, the (N2 − 1)× (N2 − 1) matrices of the SU(N) generators go to those of the Poisson algebra in the large N limit. However, it is not the case for the N × N matrices in the fundamental representation.

Based on a completely distributive lattice M , we propose new fuzzification approach to module, which leads the concept of an id="M2"> -hazy module. Different from traditional that defines fuzzy algebra as subset classical algebra, introduce id="M3"> module by fuzzifications algebraic operations. Then, investigate fundam...

We describe geometric non-commutative formal groups in terms of a geometric commutative formal group with a Poisson structure on its splay algebra. We describe certain natural properties of such Poisson structures and show that any such Poisson structure gives rise to a non-commutative formal group. We describe geometric non-commutative formal groups in terms of a geometric commutative formal g...