Computation of the homology of the complexes of finite Verma modules for \(K'_4\). (English) Zbl 1536.17030
Summary: We compute the homology of the complexes of finite Verma modules over the annihilation superalgebra \(\mathcal{A}(K'_4)\), associated with the conformal superalgebra \(K'_4\), obtained in [the author and F. Caselli, J. Math. Phys. 63, No. 9, Article ID 091701, 41 p. (2022; Zbl 1509.17007)]. We use the computation of the homology in order to provide an explicit realization of all the irreducible quotients of finite Verma modules over \(\mathcal{A}(K'_4)\).
MSC:
| 17B55 | Homological methods in Lie (super)algebras |
| 08A05 | Structure theory of algebraic structures |
| 17B10 | Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) |
| 17B65 | Infinite-dimensional Lie (super)algebras |
| 17B70 | Graded Lie (super)algebras |
Citations:
Zbl 1509.17007References:
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