Título
Determinants of finite potent endomorphisms, symbols and reciprocity laws
Autor(es)
Palabras clave
Infinite determinant,
Finite potent endomorphism
Hilbert space
Central extension of groups
Clasificación UNESCO
12 Matemáticas
1201 Álgebra
Fecha de publicación
2013-07-01
Editor
Elsevier
Citación
Daniel Hernández Serrano, Fernando Pablos Romo, Determinants of finite potent endomorphisms, symbols and reciprocity laws, Linear Algebra and its Applications, Volume 439, Issue 1, 2013, Pages 239-261, ISSN 0024-3795, https://doi.org/10.1016/j.laa.2013.02.033. (https://www.sciencedirect.com/science/article/pii/S002437951300164X)
Resumen
[EN]The aim of this paper is to offer an algebraic definition of infinite determinants of finite potent endomorphisms using linear algebra techniques. It generalizes Grothendieck’s determinant for finite rank endomorphisms and is equivalent to the classic analytic definitions. 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.
URI
ISSN
0024-3795. 1873-1856
DOI
10.1016/j.laa.2013.02.033
Versión del editor
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