How Euler would compute the Euler-Poincaré characteristic of a Lie superalgebra

Details How Euler would compute the Euler-Poincaré characteristic of a Lie superalgebra How Euler would compute the Euler-Poincaré characteristic of a Lie superalgebra

2008-12-11

arxiv.org/abs/0812.2255v3

Expositiones Mathematicae 29 (2011), 345-360

Mathematics

K-Theory and Homology

v3: minor English corrections

Scientific paper

10.1016/j.exmath.2011.06.002

The Euler-Poincar\'e characteristic of a finite-dimensional Lie algebra vanishes. If we want to extend this result to Lie superalgebras, we should deal with infinite sums. We observe that a suitable method of summation, which goes back to Euler, allows to do that, to a certain degree. The mathematics behind it is simple, we just glue the pieces of elementary homological algebra, first-year calculus and pedestrian combinatorics together, and present them in a (hopefully) coherent manner.

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