We provide a description of the ordinary derivations of the Grassmann algebra of a vector space of countable dimension, adding details to an earlier description due to Djokovič. More precisely, we prove that the derivation algebra Der(E) of the Grassmann algebra E decomposes into a direct sum of a maximal abelian Lie subalgebra D and a Lie subalgebra Δ, with D properly containing the abelian ideal of inner derivations. In the last short section of the paper, the kernels of some derivations involved in the investigations about the differential polynomial identities of E are computed.
A short note on derivations of the Grassmann algebra
Nardozza Vincenzo
2026-01-01
Abstract
We provide a description of the ordinary derivations of the Grassmann algebra of a vector space of countable dimension, adding details to an earlier description due to Djokovič. More precisely, we prove that the derivation algebra Der(E) of the Grassmann algebra E decomposes into a direct sum of a maximal abelian Lie subalgebra D and a Lie subalgebra Δ, with D properly containing the abelian ideal of inner derivations. In the last short section of the paper, the kernels of some derivations involved in the investigations about the differential polynomial identities of E are computed.File in questo prodotto:
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