On infinite determinants of finite potent endomorphisms

Details On infinite determinants of finite potent endomorphisms On infinite determinants of finite potent endomorphisms

2010-11-09

arxiv.org/abs/1011.2044v2

Mathematics

Rings and Algebras

Version 2. Structural changes

Scientific paper

The aim of this paper is to offer an algebraic definition of infinite determinants of finite potent endomorphisms. It generalizes Grothendieck's determinant for finite rank endomorphisms on infinite-dimensional vector spaces, and is equivalent to the classic analytic definitions. Moreover, the theory can be interpreted as a multiplicative analogue to Tate's formalism of abstract residues in terms of traces of finite potent linear operators on infinite-dimensional vector spaces, and allows us to relate Tate's theory to the Segal-Wilson pairing in the context of loop groups.

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