abstract Srni 2019

Localization approach to noncommutative flag varieties

SrnĂ 16.1. 2019. 16.30-16.55

It is common to look for coset spaces of Hopf algebras by consideration of coinvariants for coactions of quotient Hopf algebras. Usually those are too small, and one may need to localize in a way compatible with coaction to ensure sufficiently many coinvariants to describe the quantum coset spaces. In a work with G. Bohm, we have proved when such (and much more general) coset spaces provide noncommutative schemes, with principal examples yielding a construction of quantum group flag varieties. I shall sketch the example of what I call the universal noncommutative flag varieties which contain the quantum flag varieties as their small subvarieties but which do not require q-commutation relations, but are closer to certain Cohn localizations of free associative algebras. This example is fundamental in providing a geometric interpretations of the quasideterminant calculus of Gelfand and Retakh.

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