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Original scientific paper
https://doi.org/10.21857/yrvgqtpk89

A note on the affine vertex algebra associated to gl(1|1) at the critical level and its generalizations

Dražen Adamović ; Department of Mathematics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia

Fulltext: english, pdf (220 KB) pages 75-87 downloads: 213* cite
APA 6th Edition
Adamović, D. (2017). A note on the affine vertex algebra associated to gl(1|1) at the critical level and its generalizations. Rad Hrvatske akademije znanosti i umjetnosti, (532=21), 75-87. https://doi.org/10.21857/yrvgqtpk89
MLA 8th Edition
Adamović, Dražen. "A note on the affine vertex algebra associated to gl(1|1) at the critical level and its generalizations." Rad Hrvatske akademije znanosti i umjetnosti, vol. , no. 532=21, 2017, pp. 75-87. https://doi.org/10.21857/yrvgqtpk89. Accessed 20 Oct. 2019.
Chicago 17th Edition
Adamović, Dražen. "A note on the affine vertex algebra associated to gl(1|1) at the critical level and its generalizations." Rad Hrvatske akademije znanosti i umjetnosti , no. 532=21 (2017): 75-87. https://doi.org/10.21857/yrvgqtpk89
Harvard
Adamović, D. (2017). 'A note on the affine vertex algebra associated to gl(1|1) at the critical level and its generalizations', Rad Hrvatske akademije znanosti i umjetnosti, (532=21), pp. 75-87. https://doi.org/10.21857/yrvgqtpk89
Vancouver
Adamović D. A note on the affine vertex algebra associated to gl(1|1) at the critical level and its generalizations. Rad Hrvatske akademije znanosti i umjetnosti [Internet]. 2017 [cited 2019 October 20];(532=21):75-87. https://doi.org/10.21857/yrvgqtpk89
IEEE
D. Adamović, "A note on the affine vertex algebra associated to gl(1|1) at the critical level and its generalizations", Rad Hrvatske akademije znanosti i umjetnosti, vol., no. 532=21, pp. 75-87, 2017. [Online]. https://doi.org/10.21857/yrvgqtpk89

Abstracts
In this note we present an explicit realization of the affine vertex algebra V^cri(gl(1|1)) inside of the tensor product F ⊗ M where F is a fermionic verex algebra and M is a commutative vertex algebra. This immediately gives an alternative description of the center of V^cri(gl(1|1)) as a subalgebra M_0 of M. We reconstruct the Molev-Mukhin formula for the Hilbert-Poincare series of the center of V^cri(gl(1|1)). Moreover, we construct a family of irreducible Vcri(gl(1|1))-modules realized on F and parameterized by χ+, χ- ∈ C((z)). We propose a generalization of V^cri(gl(1|1)) as a critical level version of the super W_{1+∞} vertex algebra.

Keywords
Vertex algebras; affine Lie superalgebras; critical level; W-algebras

Projects
HRZZ / IP / IP-2013-11-2634 / ACMVAT - Algebraic and combinatorial methods in vertex algebra theory

Hrčak ID: 186431

URI
https://hrcak.srce.hr/186431

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