Glasnik Matematicki, Vol. 52, No. 2 (2017), 275-288.

THE CENTRALIZER OF K IN U(𝔤) ⊗ C(𝔭) FOR THE GROUP SOE(4,1)

Ana Prlić

Department of Mathematics, University of Zagreb, 10 000 Zagreb, Croatia
e-mail: anaprlic@math.hr

Abstract.   Let G be the Lie group SOe(4,1), with maximal compact subgroup K = S(O(4) × O(1))e≅ SO(4). Let 𝔤 =𝔰𝔬(5,ℂ) be the complexification of the Lie algebra 𝔤0 = 𝔰𝔬(4,1) of G, and let U(𝔤) be the universal enveloping algebra of 𝔤. Let 𝔤 = 𝔨 ⊕ 𝔭 be the Cartan decomposition of 𝔤, and C(𝔭) the Clifford algebra of 𝔭 with respect to the trace form B(X, Y) = tr(XY) on 𝔭. In this paper we give explicit generators of the algebra (U(𝔤) ⊗ C(𝔭))K.

2010 Mathematics Subject Classification.   22E47, 22E46.

Key words and phrases.   Lie group, Lie algebra, representation, Dirac operator, Dirac cohomology.


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DOI: 10.3336/gm.52.2.07


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