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arXiv · 0812.2255

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

Pasha Zusmanovich
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Abstract

The Euler-Poincaré 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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Pasha Zusmanovich. 2012-01-27. How Euler would compute the Euler-Poincaré characteristic of a Lie superalgebra. https://doi.org/10.1016/j.exmath.2011.06.002

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