Quantum Clifford-Hopf Algebras for Even Dimensions

Gorenstein global dimensions for Hopf algebra actions

Let $H$ be a Hopf algebra and $A$ an $H$-bimodule algebra‎. ‎In this paper‎, ‎we investigate Gorenstein global dimensions for Hopf‎ ‎algebras and twisted smash product algebras $Astar H$‎. ‎Results from‎ ‎the literature are generalized‎. 

Quantum Doubles From A Class Of Noncocommutative Weak Hopf Algebras

The concept of biperfect (noncocommutative) weak Hopf algebras is introduced and their properties are discussed. A new type of quasi-bicrossed products are constructed by means of weak Hopf skew-pairs of the weak Hopf algebras which are generalizations of the Hopf pairs introduced by Takeuchi. As a special case, the quantum double of a finite dimensional biperfect (noncocommutative) weak Hopf a...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

The Hidden Quantum Group of the 8–vertex Free Fermion Model: q–Clifford Algebras

We prove in this paper that the elliptic R–matrix of the eight vertex free fermion model is the intertwiner R–matrix of a quantum deformed Clifford–Hopf algebra. This algebra is constructed by affinization of a quantum Hopf deformation of the Clifford algebra. IMAFF-2/93 February 1993

Polyvector-valued Gauge Field Theories and Quantum Mechanics in Noncommutative Clifford Spaces

The basic ideas and results behind polyvector-valued gauge field theories and Quantum Mechanics in Noncommutative Clifford spaces are presented. The star products are noncommutative but associative up to second order only. The construction of Noncommutative Clifford-space gravity as polyvector-valued gauge theories of twisted diffeomorphisms in Clifford-spaces would require quantum Hopf algebra...