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See detailBrackets with (τ, σ )-derivations and (p, q)-deformations of Witt and Virasoro algebras
Elchinger, Olivier UL; Lundengård, Karl; Mahklouf, Abdenacer et al

in Forum Mathematicum (2015)

The aim of this paper is to study some brackets defined on (τ, σ )-derivations sat- isfying quasi-Lie identities. Moreover, we provide examples of (p, q)-deformations of Witt and Virasoro algebras as well ... [more ▼]

The aim of this paper is to study some brackets defined on (τ, σ )-derivations sat- isfying quasi-Lie identities. Moreover, we provide examples of (p, q)-deformations of Witt and Virasoro algebras as well as sl(2) algebra. These constructions gen- eralize the results obtained by Hartwig, Larsson and Silvestrov on σ -derivations, arising in connection with discretizations and deformations of algebras of vector fields. [less ▲]

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See detailStudy of formality for the Heisenberg algebra
Elchinger, Olivier UL

E-print/Working paper (2014)

In this paper, we compute the Chevalley-Eilenberg cohomology of the three-dimensional Heisenberg Lie algebra with values in its universal enveloping algebra. We also compute the Schouten brackets on ... [more ▼]

In this paper, we compute the Chevalley-Eilenberg cohomology of the three-dimensional Heisenberg Lie algebra with values in its universal enveloping algebra. We also compute the Schouten brackets on cochains and cohomology level in order to write the formality equations. It turns out that there is no formality, and that the perturbed L∞ structure on the cohomology has non-trivial terms in infinitely many degrees. [less ▲]

Detailed reference viewed: 59 (11 UL)