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...

Miriam Cohen raised the question whether the smash product of a semisimple Hopf algebra and a semiprime module algebra is semiprime. In this paper we show that the smash product of a commutative semiprime module algebra over a semisimple cosemisimple Hopf algebra is semiprime. In particular we show that the central H-invariant elements of the Martindale ring of quotients of a module algebra for...

In an attempt to study the zero divisors in Hopf algebras, we study four non-trivial examples of nongroup ring infinite Hopf algebras and show that a variant of Kaplansky’s classical zero divisor conjecture holds for these four Hopf algebras. In particular we proof that the Hopf algebra CG has no non-trivial zero-divisors for any infinite finitely generated group G. We then consider the zero di...

We show that when a co-involutive Hopf C *-algebra S coacts via δ on a C *-algebra A, there exists a full crossed product A × δ S, with universal properties analogous to those of full crossed products by locally compact groups. The dual Hopf C *-algebra is then defined byˆS := C × id S.

Miriam Cohen raised the question whether the smash product of a semisimple Hopf algebra and a semiprime module algebra is semiprime. In this paper we show that the smash product of a commutative semiprime module algebra over a semisimple cosemisimple Hopf algebra is semiprime. In particular we show that the central H-invariant elements of the Martindale ring of quotients of a module algebra for...

Braided Hopf algebras have attracted much attention in both mathematics and mathematical physics (see e.g. [2][4][14][16][17][18][20][23]). The classification of finite dimensional Hopf algebras is interesting and important for their applications (see [1] [24]). Braided Hopf algebras play an important role in the classification of finite-dimensional pointed Hopf algebras (e.g. [1][2] [21]). The...

Nonlinear deformations of the enveloping algebra of su(2), involving two arbitrary functions of J0 and generalizing the Witten algebra, were introduced some time ago by Delbecq and Quesne. In the present paper, the problem of endowing some of them with a Hopf algebraic structure is addressed by studying in detail a specific example, referred to as Aq (1). This algebra is shown to possess two se...

We consider an inductive scheme for quantized enveloping algebras, arising from certain inclusions of the associated root data. These inclusions determine an algebra-subalgebra pair with the subalgebra also a quantized enveloping algebra, and we want to understand the structure of the “difference” between the algebra and the subalgebra. Our point of view treats the background field and quantiza...