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Cohomology of psl(n|n) in trivial and in adjoint representations
Abstract
We compute the cohomology of the projective special linear Lie superalgebra psl(n|n) over a field of characteristic zero in trivial and in adjoint coefficients in full detail through its associated Hochschild--Serre spectral sequences. Applications in physics exist for its real form, the projective special unitary Lie superalgebra psu(n|n) --- in particular, psu(2,2|4) for AdS/CFT. We also find the cohomology of sl(m|n) in trivial coefficients along the way and we point out a discrepancy with a previous statement in the literature. We present the explicit cohomology groups of low degree for nleqslant4.
Related
- Monodromy and big quantum cohomology of hyperplane sections of (co)adjoint varieties
- R-trivial Galois cohomology classes and cohomological p-dimension
- Modular class of Lie ∞-algebroids and adjoint representations
- Permutation Representations on Cohomology of Toric Varieties
- Fixed point properties and cohomology of Banach representations of arithmetic groups
BibTeX
@misc{ferreira2026cohomology,
title = {{Cohomology of $\mathfrakpsl(n|n)$ in trivial and in adjoint representations}},
author = {Thiago Oliveira Ferreira},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22598},
eprint = {2609.22598},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22598},
}
RIS
TY - UNPB
TI - Cohomology of psl(n|n) in trivial and in adjoint representations
AU - Thiago Oliveira Ferreira
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.22598
UR - https://arxiv.org/abs/2609.22598
AB - We compute the cohomology of the projective special linear Lie superalgebra psl(n|n) over a field of characteristic zero in trivial and in adjoint coefficients in full detail through its associated Hochschild--Serre spectral sequences. Applications in physics exist for its real form, the projective special unitary Lie superalgebra psu(n|n) --- in particular, psu(2,2|4) for AdS/CFT. We also find the cohomology of sl(m|n) in trivial coefficients along the way and we point out a discrepancy with a previous statement in the literature. We present the explicit cohomology groups of low degree for nleqslant4.
ER -