Grothendieck rings of Queer Lie superalgebras

We determine the Grothendieck rings of category finite-dimensional modules over Queer Lie superalgebras via their characters. In particular, we show that Q \mathbb {Q} -span ring characters supergroup alttext="upper Q left-parenthesis n right-parenthesis"> Q ( n stretchy="false">) encoding="application/x-tex">Q(n) is isomorphic to Laurent polynomials in alttext="x 1 comma ellipsis x Subscript Baseline"> x 1 , … encoding="application/x-tex">x_{1},\ldots ,x_{n} for which evaluation minus Baseline equals t"> −<!-- − <mml:mo>= t encoding="application/x-tex">x_{n-1}=-x_{n}=t independent alttext="t"> encoding="application/x-tex">t . thus complete description all classical superalgebras.