What question did this study set out to answer?

The aim is to compute the cohomology of Lie algebras of maximal class over the field Z2 and explore their properties.

March 29, 2026Open Access

Cohomology of N-Graded Lie Algebras of Maximal Class over Z2

YNY. NikolayevskyLa Trobe University ITI. Tsartsaflis

Key Points

The aim is to compute the cohomology of Lie algebras of maximal class over the field Z2 and explore their properties.
Computed cohomology rings of m0 and m2 with trivial coefficients.
Analyzed both infinite-dimensional and finite-dimensional cases.
Determined the first three Betti numbers of m0(n) and m2(n).
Cohomology rings H*(m0) and H*(m2) are isomorphic in the infinite-dimensional case.
Described cohomology rings completely in contrast to characteristic zero cases.
Identified the first three Betti numbers for the finite-dimensional Lie algebras m0(n) and m2(n).

Abstract

We compute the cohomology with trivial coefficients of Lie algebras m 0 and m 2 of maximal class over the field Z 2 .In the infinite-dimensional case, we show that the cohomology rings H * (m 0 ) and H * (m 2 ) are isomorphic, in contrast with the case of the ground field of characteristic zero, and we obtain a complete description of them.In the finite-dimensional case, we find the first three Betti numbers of m 0 (n) and m 2 (n) over Z 2 .

KI fragen

Bookmark

View Full Paper