Lengths of finite dimensional representations of PBW algebras

DOI10.1016/J.LAA.2004.08.006zbMath1068.15015arXivmath/0309403OpenAlexW2040423039MaRDI QIDQ1765913

M. Darnall, David Constantine

Publication date: 23 February 2005

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0309403

zbMATH Keywords

representations of quantum groupsrepresentations of Lie algebraslengths of representationsPBW setsPoincaré-Birkhoff-Witt algebra

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Algebraic systems of matrices (15A30)

Related Items (8)

The effect of assuming the identity as a generator on the length of the matrix algebra ⋮ Lengths of quasi-commutative pairs of matrices ⋮ The realizability problem for the values of the length function of quasi-commuting matrix pairs ⋮ The length function and matrix algebras ⋮ ON THE LENGTHS OF PAIRS OF COMPLEX MATRICES OF SIZE SIX ⋮ Length realizability for pairs of quasi-commuting matrices ⋮ On the relationship between the length of an algebra and the index of nilpotency of its Jacobson radical. ⋮ On the lengths of irreducible pairs of complex matrices

Cites Work

• An upper bound for the length of a finite-dimensional algebra
• An application of the Cayley-Hamilton theorem to matrix polynomials in several variables
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