In this paper we study the concept of ph-biatness ofa Banach algebra A, where ph is a continuous homomorphism on A.We prove that if ph is a continuous epimorphism on A and A hasa bounded approximate identity and A is ph- biat, then A is ph-amenable. In the case where ph is an isomorphism on A we showthat the ph- amenability of A implies its ph-biatness.

Consider a semisimple complex Lie algebra g and its universal enveloping algebra U(g). In order to study unitary representations of semisimple Lie groups, Harish-Chandra ([HC1] Part III) established an isomorphism between the center Z(g) of U(g) and the algebra of invariant polynomials C[t] . Here, t ⊆ g is a Cartan subspace and W is the Weyl group of g. This is one of the most basic results in...

Let L be a restricted Lie algebra with the restricted enveloping algebra u(L) over a perfect field of positive characteristic p. The restricted isomorphism problem asks what invariants of L are determined by u(L). This problem is the analogue of the modular isomorphism problem for finite p-groups. Bagiński and Sandling have given a positive answer to the modular isomorphism problem for metacycl...

For any 1-reduced simplicial set K we define a canonical, coassociative coproduct on ΩC(K), the cobar construction applied to the normalized, integral chains on K, such that any canonical quasi-isomorphism of chain algebras from ΩC(K) to the normalized, integral chains on GK, the loop group of K, is a coalgebra map up to strong homotopy. Our proof relies on the operadic description of the categ...

We characterize the structure of a seven-dimensional Lie algebra with non-trivial center endowed closed G$_2$-structure. Using this result, we classify all unimodular algebras admitting G$_2$-structures, up to isomorphism, and show that six them arise as contactization symplectic algebra. Finally, prove every semi-algebraic soliton on must be expanding, determine dimension at least two admit so...

We show that if T is an isometry (as metric spaces) from an open subgroup of the group of the invertible elements in a unital semisimple commutative Banach algebra onto an open subgroup of the group of the invertible elements in a unital Banach algebra, then T (1)T is an isometrical group isomorphism. In particular, T (1)T is extended to an isometrical real algebra isomorphism from A onto B.

and Applied Analysis 3 in the middle variable, and associative in the sense that x, y, z,w, v x, w, z, y , v x, y, z , w, v , and satisfies ‖ x, y, z ‖ ≤ ‖x‖ · ‖y‖ · ‖z‖ and ‖ x, x, x ‖ ‖x‖ see 45, 47 . Every left Hilbert C∗-module is a C∗-ternary algebra via the ternary product x, y, z : 〈x, y〉z. If a C∗-ternary algebra A, ·, ·, · has an identity, that is, an element e ∈ A such that x x, e, e ...

Let M be a smooth Fredholm manifold modeled on a separable infinite-dimensional Euclidean space E with Riemannian metric g. Given an augmented Fredholm filtration F of M by finite-dimensional submanifolds {Mn}∞n=k, we associate to the triple (M, g,F) a non-commutative direct limit C-algebra A(M, g,F) = lim −→ A(Mn) that can play the role of the algebra of functions vanishing at infinity on the ...

We define the Hopf algebra structure on the Grothendieck group of finitedimensional polynomial representations of Uq ĝlN in the limit N → ∞. The resulting Hopf algebra Rep Uq ĝl∞ is a tensor product of its Hopf subalgebras Repa Uqĝl∞, a ∈ C/q. When q is generic (resp., q is a primitive root of unity of order l), we construct an isomorphism between the Hopf algebra Repa Uq ĝl∞ and the algebra of...