FAITHFUL REPRESENTATIONS OF MINIMAL DIMENSION OF CURRENT HEISENBERG LIE ALGEBRAS
2009 ◽
Vol 20
(11)
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pp. 1347-1362
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Keyword(s):
Given a Lie algebra 𝔤 over a field of characteristic zero k, let μ(𝔤) = min{dim π : π is a faithful representation of 𝔤}. Let 𝔥m be the Heisenberg Lie algebra of dimension 2m + 1 over k and let k [t] be the polynomial algebra in one variable. Given m ∈ ℕ and p ∈ k [t], let 𝔥m, p = 𝔥m ⊗ k [t]/(p) be the current Lie algebra associated to 𝔥m and k [t]/(p), where (p) is the principal ideal in k [t] generated by p. In this paper we prove that [Formula: see text]. We also prove a result that gives information about the structure of a commuting family of operators on a finite dimensional vector space. From it is derived the well-known theorem of Schur on maximal abelian subalgebras of 𝔤𝔩(n, k ).
2018 ◽
Vol 17
(11)
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pp. 1850212
1997 ◽
Vol 56
(3)
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pp. 483-488
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1978 ◽
Vol 21
(4)
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pp. 483-489
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1988 ◽
Vol 112
◽
pp. 153-169
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1982 ◽
Vol 25
(2)
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pp. 133-139
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1995 ◽
Vol 138
◽
pp. 113-140
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