Partial representation theory

Abstract: The non-associativity in this talk concerns actions rather than algebras. In the case of a so-called partial representation of a group, or more generally of a Hopf algebra, the usual associativity constraint for the associated action is weakened in the sense that it is only valid in the presence of a “witness”. This weaker version of associativity can, however, still be interpreted as associativity in the usual sense, but the price to pay for this is that the group needs to be replaced by a groupoid (and the Hopf algebra by a Hopf algebroid). The category of partial representations for a given group or Hopf algebra has many interesting properties and provides us with more information than the usual representation category, which it contains as a full subcategory. In this talk, I want to present an overview of this theory, some recent developments, and remaining challenges.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar