2020/09/16 by Shlomo Gelaki, Gelaki, Shlomo
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2009.07760
We use \citeG to study the algebra structure of twisted cotriangular Hopf algebras JO(G)J, where J is a Hopf 2-cocycle for a connected nilpotent algebraic group G over ℂ. In particular, we show that JO(G)J is an affine Noetherian domain with Gelfand-Kirillov dimension dim(G), and that if G is unipotent and J is supported on G, then JO(G)J≅ U(\g) as algebras, where \g=\rm Lie(G). We also determine the finite dimensional irreducible representations of JO(G)J, by analyzing twisted function algebras on (H,H)-double cosets of the support H⊂ G of J. Finally, we work out several examples to illustrate our results.