Homology of Lie Algebras of Orthogonal and Symplectic Generalized Jacobi Matrices

TL;DR

This paper computes the homology of Lie algebras formed by generalized Jacobi matrices of types B, C, and D over certain associative algebras, extending understanding of their algebraic structure.

Contribution

It provides explicit homology calculations for Lie algebras of generalized Jacobi matrices of types B, C, and D, which was previously unexplored.

Findings

Homology computed for Lie algebras of types B, C, D

Results applicable over fields of characteristic zero

Advances understanding of algebraic structures of these Lie algebras

Abstract

In this note, we compute the homology with trivial coefficients of Lie algebras of generalized Jacobi matrices of type $B, C$ and $D$ over an associative unital $k$-algebra with $k$ being a field of characteristic $0$.