2001/12/20 by S. Grillo, Grillo, S., H. Montani +1
Mathematics · Physics and Astronomy · #46L52 #58B32 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #math-ph #math.MP #math.QA #msc:46L52 #msc:58B32
paper · pdf · doi:10.48550/arxiv.math/0112233
23 pages; Added references and minor changes (including more accurate terminology)
arxiv created 2003/06/27 · arxiv updated 2009/11/30
Adapting the idea of twisted tensor products to the category of finitely generated algebras, we define on its opposite, the category QLS of quantum linear spaces, a family of objects hom(B,A)op, one for each pair Aop,Bop there, with analogous properties to its internal Hom ones, but representing spaces of transformations whose coordinate rings hom(B,A) and the ones of their respective domains Bop do not commute among themselves. The mentioned non commutativity is controlled by a collection of twisting maps τA,B. We show that the (bi)algebras end(A)=hom(A,A), under certain circumstances, are 2-cocycle twistings of the quantum semigroups end(A) in the untwisted case. This fact generalizes the twist equivalence (at a semigroup level) between, for instance, the quantum groups GLq(n) and their multiparametric versions GLq,ϕ(n).