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Generalized Casimir operators for loop Lie superalgebras
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- Canadian Mathematical Bulletin , First View
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- 27 January 2025, pp. 1-17
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Let
$\mathfrak{g}$ be the queer superalgebra 
$\operatorname {\mathfrak{q}}(n)$ over the field of complex numbers 
$\mathbb C$. For any associative, commutative, and finitely generated 
$\mathbb C$-algebra A with unity, we consider the loop Lie superalgebra 
$\mathfrak{g} \otimes A$. We define a class of central operators for 
$\mathfrak{g} \otimes A$, which generalizes the classical Gelfand invariants. We show that they generate the algebra 
$U(\mathfrak{g} \otimes A)^{\mathfrak{g}}$. We also show that there are no non-trivial 
$\mathfrak{g}$-invariants of 
$U(\mathfrak{g} \otimes A)$ where 
$\mathfrak{g}=\mathfrak{p}(n)$, the periplectic Lie superalgebra.
Casimir Operators and Nilpotent Radicals
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- Journal:
- Canadian Mathematical Bulletin / Volume 55 / Issue 3 / 01 September 2012
- Published online by Cambridge University Press:
- 20 November 2018, pp. 579-585
- Print publication:
- 01 September 2012
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