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Register a new userThe structures of Hopf $ast$-algebra on Radford algebras
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We investigate the structures of Hopf $ast$-algebra on the Radford algebras over $mathbb {C}$. All the $*$-structures on $H$ are explicitly given. Moreover, these Hopf $*$-algebra structures are classified up to equivalence.
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Let $H$ be a finite dimensional semisimple Hopf algebra, $A$ a differential graded (dg for short) $H$-module algebra. Then the smash product algebra $A#H$ is a dg algebra. For any dg $A#H$-module $M$, there is a quasi-isomorphism of dg algebras: $mathrm{RHom}_A(M,M)#Hlongrightarrow mathrm{RHom}_{A#H}(Mot H,Mot H)$. This result is applied to $d$-Koszul algebras, Calabi-Yau algebras and AS-Gorenstein dg algebras
Let $Bbbk$ be a base field of characteristic $p>0$ and let $U$ be the restricted enveloping algebra of a 2-dimensional nonabelian restricted Lie algebra. We classify all inner-faithful $U$-actions on noetherian Koszul Artin-Schelter regular algebras of global dimension up to three.
We determine commutative post-Lie algebra structures on some infinite-dimensional Lie algebras. We show that all commutative post-Lie algebra structures on loop algebras are trivial. This extends the results for finite-dimensional perfect Lie algebras. Furthermore we show that all commutative post-Lie algebra structures on affine Kac--Moody Lie algebras are almost trivial.
We investigate a method of construction of central deformations of associative algebras, which we call centrification. We prove some general results in the case of Hopf algebras and provide several examples.
We study actions of semisimple Hopf algebras H on Weyl algebras A over a field of characteristic zero. We show that the action of H on A must factor through a group algebra; in other words, if H acts inner faithfully on A, then H is cocommutative. The techniques used include reduction modulo a prime number and the study of semisimple cosemisimple Hopf actions on division algebras.
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