Varieties for Modules of Quantum Elementary Abelian Groups
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We define a rank variety for a module of a noncocommutative Hopf algebra A = G where = k[X1,, X m]/(X1,, Xm), G = (/ )m and char k does not divide , in terms of certain subalgebras of A playing the role of "cyclic shifted subgroups". We show that the rank variety of a finitely generated module M is homeomorphic to the support variety of M defined in terms of the action of the cohomology algebra of A. As an application we derive a theory of rank varieties for the algebra . When =2, rank varieties for -modules were constructed by Erdmann and Holloway using the representation theory of the Clifford algebra. We show that the rank varieties we obtain for -modules coincide with those of Erdmann and Holloway. 2008 Springer Science+Business Media B.V.
Algebras and Representation Theory
author list (cited authors)
Pevtsova, J., & Witherspoon, S.
complete list of authors
Pevtsova, Julia||Witherspoon, Sarah