Hopf algebras of discrete co-representation type

Abstract: Hopf algebra is an important topic in geometric representation theory. A basic algebra is of finite representation type if there are only finitely many non-isomorphic indecomposable representations. Basic Hopf algebras of finite representation type have been classified by Liu and Li in 2004. As algebras, they are just copies of Nakayama algebras. A pointed coalgebra is of discrete co-representation type, if there are only finitely many non-isomorphic indecomposable co-representations for each dimension vector. We are trying to classify pointed Hopf algebras of discrete co-representation type. We first classify their Ext-quivers as coalgebras. Then we compute their algebra structures for each case. This is a joint work with Miodrag Iovanov, Emre Sen and Alexander Sistko.

commutative algebraalgebraic geometrycombinatoricsrings and algebrasrepresentation theory

Audience: researchers in the topic

Geometry, Algebra, Singularities, and Combinatorics

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