noncommutative geometry@n – the trade contains applications to the material developed in volume 1 - the tools to moduli spaces, quiver varieties and singularities. It details the representation... More > theory of Cayley-smooth and Quillen-smooth algebras by studying the geometry of the quotient varieties and relating the Hesselink stratification of their nullcones to moduli spaces of quiver-representations. Further, it explains by examples the theory of noncommutative differential forms leading to the application of the necklace Lie algebra to coadjoint orbit results.
This is a two-year old preliminary version. An extended, updated and corrected version will appear in the fall of 2007 with Chapman&Hall. Use this version only for private use.< Less
noncommutative geometry@n – the tools, contains the material a starting researcher needs to enter this fascinating new topic. Motivated by examples from representation theory of algebras, it... More > initiates the reader to as different topics as : geometric invariant theory, etale cohomology, Brauer groups and rings satisfying polynomial identities. This volume contains the geometric reconstruction result for Cayley-Hamilton algebras, due to Claudio Procesi, and the etale local classification of Cayley-smooth algebras via marked quiver-settings. The second volume will focuss on applications to moduli spaces, quiver varieties and singularities.
This is a two-year old preliminary version. An extended, updated and corrected version will appear in the fall of 2007 with Chapman&Hall. Use this version only for private use.< Less
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