Algebra Learning Seminar

Hongdi Huang, Department of Pure Mathematics, University of Waterloo

Panov asked a question: given a field F and a Hopf F-algebra R, for which algebra automorphisms \sigma and \sigma-derivations \delta can the skew polynomial algebra T=R[x, \sigma, \delta] be given a structure of Hopf algebra extending the given structure on R? In this talk, we will discuss the answers with the assumption that \Delta(x)=a\otimes x + x\otimes b, or \Delta(x)=a\otimes x+ x\otimes b +v(x\otimes x)+ w, where a, b  are group like elements in R, and v, w\in R\otimes R, \Delta is the coproduct of Hopf algebra T (if T has the Hopf algebra structure). In particular, if R is connect (i. e. the coradical of R is k), then T will satisfy the assumption. 

MC 5413