Search Results - "Musson, Ian M."

Hochschild Cohomology and Deformations of Clifford-Weyl Algebras by Musson, Ian M.

“…We give a complete study of the Clifford-Weyl algebra C(n,2k) from Bose-Fermi statistics, including Hochschild cohomology (with coefficients in itself). We…”
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Finite dimensional representations of invariant differential operators by Musson, Ian M., Rueda, Sonia L.

“…Let k be an algebraically closed field of characteristic 0, Y=k^{r}\times {(k^{\times})}^{s}, and let G be an algebraic torus acting diagonally on the ring of…”
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P.I. envelopes of classical simple Lie superalgebras by Musson, Ian M.

“…Let \mathfrak{g} be a classical simple Lie superalgebra. We describe the prime ideals P in the enveloping algebra U(\mathfrak{g}) such that U(\mathfrak{g})/P…”
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Explicit expressions for Šapovalov elements in Type A by Musson, Ian M.

“…We give explicit expressions for Šapovalov elements in Type A Lie algebras and superalgebras. Explicit expressions were already given in [11] Section 9, using…”
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Shapovalov elements for Uq(sl(N+1)) by Catoiu, Stefan, Musson, Ian M.

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Invariant Differential Operators and FCR Factors of Enveloping Algebras by Musson, Ian M., Willenbring, Jeb F.

“…If is a semisimple Lie algebra, we describe the prime factors of ( ) that have enough finite dimensional modules. The proof depends on some combinatorial facts…”
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Noetherian down-up algebras by Kirkman, Ellen, Musson, Ian M., Passman, D. S.

“…Down-up algebras A= A(\alpha ,\beta ,\gamma ) were introduced by G. Benkart and T. Roby to better understand the structure of certain posets. In this paper, we…”
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On the Goldie Quotient Ring of the Enveloping Algebra of a Classical Simple Lie Superalgebra by Musson, Ian M

“…If g is a classical simple Lie superalgebra (g≠P(n)), the enveloping algebra U(g) is a prime ring and hence has a simple artinian ring of quotients Q(U(g)) by…”
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Crystal Bases forUq(osp(1, 2r)) by Musson, Ian M, Zou, Yi Ming

“…We construct Z2-graded crystal bases for the quantized universal enveloping algebra of the Lie superalgebraosp(1,2r). We show that, like the crystal bases in…”
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Some Lie superalgebras associated to the Weyl algebras by Musson, Ian M.

“…Let {\mathfrak{g}} be the Lie superalgebra osp(1,2r). We show that there is a surjective homomorphism from U({\mathfrak{g}}) to the r^{th} Weyl algebra A_{r},…”
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The Weyl groupoid in Type A, Young diagrams and Borel subalgebras by Musson, Ian M

“…Let $\mathtt{k}$ be an algebraically closed field of characteristic zero. Let ${\stackrel{{\rm o}}{{\mathfrak{g}}}$ be the Lie superalgebra…”
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Links between cofinite prime ideals in quantum function algebras by Musson, Ian M.

“…We describe the skew primitive elements in a multiparameter enveloping algebraU=Uq,p−1 (g) and the links between cofinite maximal ideals in the corresponding…”
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On the geometry of algebras related to the Weyl groupoid by Musson, Ian M

“…Let $\mathtt{k}$ be an algebraically closed field of characteristic zero. Let $\mathfrak{g} $ be a finite dimensional classical simple Lie superalgebra over…”
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Weyl groupoids and superalgebraic sets by Musson, Ian M

“…This paper is a contribution to the study of the geometry of algebras related the Weyl groupoid initiated in \cite{M22}. The Nullstellensatz gives a bijection…”
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Rings of Differential Operators on Invariant Rings of Tori by Musson, Ian M.

“…Let $k$ be an algebraically closed field of characteristic zero and $G$ a torus acting diagonally on $k^s$. For a subset $\beta$ of $s = \{1,2,\ldots,s\},…”
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Explicit expressions for \vSapovalov elements in Type A by Musson, Ian M

“…We give explicit expressions for \vSapovalov elements in Type A Lie algebras and superalgebras. Explicit expressions were already given in arXiv:1710.10528…”
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How to Construct the Lattice of Submodules of a Multiplicity free Module from Partial Information by Musson, Ian M

“…In general it is a difficult problem to construct the lattice of submodules $L(M)$ of a given module $M$. In \cite{St} R. P. Stanley outlined a method for…”
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Lie superalgebras, Clifford algebras, induced modules and nilpotent orbits by Musson, Ian M.

“…Let g be a classical simple Lie superalgebra. To every nilpotent orbit O in g 0 we associate a Clifford algebra over the field of rational functions on O . We…”
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Combinatorics of character formulas for the lie superalgebra $ \mathfrak{g}\mathfrak{l}\left( {m,n} \right) by Musson, Ian M., Serganova, Vera

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Combinatorics of character formulas for the lie superalgebra by Musson, Ian M., Serganova, Vera

“…Let be the Lie superalgebra . Algorithms for computing the composition factors and multiplicities of Kac modules for were given by the second author, [ 12 ]…”
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