Some equivariant constructions in noncommutative algebraic geometry

Details Some equivariant constructions in noncommutative algebraic geometry Some equivariant constructions in noncommutative algebraic geometry

2008-11-28

arxiv.org/abs/0811.4770v2

Georgian Mathematical Journal 16 (2009), No. 1, 183--202

Mathematics

Algebraic Geometry

20 pages, surveys basics of my long term project; v2: major revision in all parts; last section on search for Leibniz groups h

Scientific paper

We here present rudiments of an approach to geometric actions in noncommutative algebraic geometry, based on geometrically admissible actions of monoidal categories. This generalizes the usual (co)module algebras over Hopf algebras which provide affine examples. We introduce a compatibility of monoidal actions and localizations which is a distributive law. There are satisfactory notions of equivariant objects, noncommutative fiber bundles and quotients in this setup.

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