The super W1+∞ algebra with integral central charge

Creutzig T, Linshaw AR (2015)

Publication Type: Journal article

Publication year: 2015

Journal

Transactions of the American Mathematical Society American Mathematical Society

Book Volume: 367

Pages Range: 5521-5551

Journal Issue: 8

DOI: 10.1090/S0002-9947-2015-06214-X

Abstract

The Lie superalgebra SD of regular differential operators on the super circle has a universal central extension SD. For each c ∈ C, the vacuum module Mc(SD) of central charge c admits a vertex superalgebra structure,and Mc(SD) ∼= M−c(SD). The irreducible quotient Vc(SD) of the vacuummodule is known as the super W1+∞ algebra. We show that for each integern > 0, Vn(SD) has a minimal strong generating set consisting of 4n fields, andwe identify it with aW-algebra associated to the purely odd simple root systemof gl(n|n). Finally, we realize Vn(SD) as the limit of a family of commutantvertex algebras that generically have the same graded character and possess a minimal strong generating set of the same cardinality.

Involved external institutions

University of Alberta CA Canada (CA) University of Denver US United States (USA) (US)

How to cite

APA:

Creutzig, T., & Linshaw, A.R. (2015). The super W1+∞ algebra with integral central charge. Transactions of the American Mathematical Society, 367(8), 5521-5551. https://doi.org/10.1090/S0002-9947-2015-06214-X

MLA:

Creutzig, Thomas, and Andrew R. Linshaw. "The super W1+∞ algebra with integral central charge." Transactions of the American Mathematical Society 367.8 (2015): 5521-5551.

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