2002/02/20 by Sergio Grillo, Sergio D. Grillo, Grillo, Sergio D. · 1 citation
Mathematics · Physics and Astronomy · #46L52 #46L65 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #math-ph #math.MP #math.QA #msc:46L52 #msc:46L65
paper · pdf · doi:10.48550/arxiv.math/0202205
35 pages; added references and minor changes (including more accurate terminology)
openalex publication_date 2002/02/20 · arxiv created 2003/06/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Twisting process for quantum linear spaces is defined. It consists in a particular kind of globally defined deformations on finitely generated algebras. Given a quantum space (A1,A), a multiplicative cosimplicial quasicomplex C[A1] in the category Grp is associated to A1, in such a way that for every n a subclass of linear automorphisms of A⊗ n is obtained from the groups Cn[A1]. Among the elements of this subclass, the counital 2-cocycles are those which define the twist transformations. In these terms, the twisted internal coHom objects, constructed in a previous paper (cf. math.QA/0112233), can be described as twisting of the proper coHom objects, enabling us in turn to generalize the mentioned construction. The quasicomplexes C[V], V a vector space, are studied in detail, showing for instance that, when V is a coalgebra, the quasicomplexes related to Drinfeld twisting, corresponding to bialgebras generated by V, are subobjects of C[V].