Grothendieck rings of Queer Lie superalgebras

Abstract

We determine the Grothendieck rings of the category of finite-dimensional modules over Queer Lie superalgebras via their rings of characters. In particular, we show that the Q \mathbb {Q} -span of the ring of characters of the Queer Lie supergroup Q ( n ) Q(n) is isomorphic to the ring of Laurent polynomials in x 1 , … , x n x_{1},\ldots ,x_{n} for which the evaluation x n − 1 = − x n = t x_{n-1}=-x_{n}=t is independent of t t . We thus complete the description of Grothendieck rings for all classical Lie superalgebras.