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...

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...

Let G be a connected reductive algebraic group defined over an algebraically closed field F of characteristic not 2. Denote the Lie algebra of G by 9. In this paper we shall classify the isomorphism classes of ordered pairs of commuting involutorial automorphisms of G. This is shown to be independent of the characteristic of F and can be applied to describe all semisimple locally symmetric spac...

Let A be a nite dimensional hereditary algebra over a nite eld, H(A) and C(A) be respectively the Ringel-Hall algebra and the composition algebra of A. Deene r d to be the element P M] 2 H(A), where M] runs over the isomorphism classes of the regular A?modules with dimension vector d. We prove that r d and the exceptional A?modules all lie in C(A). Let K be the Kronecker algebra, P (resp. I) th...

We prove that if A is a C-algebra, then for each a ∈ A, Aa = {x ∈ A/x ≤ a} is itself a C-algebra and is isomorphic to the quotient algebra A/θa of A where θa = {(x, y) ∈ A×A/a∧ x = a∧ y}. If A is C-algebra with T , we prove that for every a ∈ B(A), the centre of A, A is isomorphic to Aa ×Aa′ and that if A is isomorphic A1 ×A2, then there exists a∈ B(A) such that A1 is isomorphic Aa and A2 is is...

In this paper we show how to construct an isomorphism between an alternative algebra A over a field of characteristic 6= 3 and its isotope A(1+c), where c is an element of Zhevlakov’s radical of A. This leads to the equivalence of any polynomial identity f = 0 in alternative algebras and the isotope identity f(s) = 0. Given an invertible element s of an alternative algebra A, we can form a new ...

In this paper, we try to attack a conjecture of Araujo and Jarosz that every bijective linear map θ between C*-algebras, with both θ and its inverse θ−1 preserving zero products, arises from an algebra isomorphism followed by a central multiplier. We show it is true for CCR C*-algebras with Hausdorff spectrum, and in general, some special C*-algebras associated to continuous fields of C*-algebras.

let $a$ be a $c^*$-algebra and $e$ be a left hilbert $a$-module. in this paper we define a product on $e$ that making it into a banach algebra and show that under the certain conditions $e$  is arens regular. we also study the relationship between derivations of $a$ and $e$.

We study the problem of matrix Lie algebra conjugacy. Lie algebras arise centrally in areas as diverse as differential equations, particle physics, group theory, and the Mulmuley–Sohoni Geometric Complexity Theory program. A matrix Lie algebra is a set L of matrices such that M1,M2 ∈ L =⇒ M1M2 − M2M1 ∈ L. Two matrix Lie algebras are conjugate if there is an invertible matrix M such that L1 = ML...

This paper is a continuation of [3] in which the first two authors have introduced the spherical Hecke algebra and the Satake isomorphism for an untwisted affine Kac-Moody group over a non-archimedian local field. In this paper we develop the theory of the Iwahori-Hecke algebra associated to these same groups. The resulting algebra is shown to be closely related to Cherednik’s double affine Hec...