Non-Weight Modules over the <i>N</i> = 1 Heisenberg–Virasoro Superalgebra

Abstract

In this paper, we mainly study free U(h)-modules over the N=1 Heisenberg–Virasoro superalgebra. We construct a family of non-weight modules that are free of rank 2 when regarded as modules over the Cartan subalgebra. Moreover, we classify the free U(h)-modules of rank 2 over the N = 1 Heisenberg–Virasoro superalgebra and provide the necessary and sufficient conditions for such g-modules to be isomorphic.

Keywords

• <i>N</i> = 1 Heisenberg–Virasoro superalgebra
• U ( h ) -module%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> free <named-content content-type="inline-formula"> <mml:math id="mm333333"> <mml:semantics> <mml:mrow> <mml:mi>U</mml:mi> <mml:mo>(</mml:mo> <mml:mi mathvariant="fraktur">h</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:semantics> </mml:math> </named-content>-module
• Cartan subalgebra