Titlebook: Clifford Algebras and Lie Theory; Eckhard Meinrenken Book 2013 Springer-Verlag Berlin Heidelberg 2013 Clifford algebras.Dirac operators.Li

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The Clifford algebra of a reductive Lie algebra,elements onto the linear subspace .. The chapter concludes with a conjecture of Kostant, expressing the resulting filtration of . in terms of the “principal TDS”. The conjecture was established in 2012 by Joseph, in conjunction with work of Alekseev–Moreau.

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Clifford algebras,terior algebra ∧(.), and in the general case the Clifford algebra can be regarded as a deformation of the exterior algebra. In this chapter after constructing the Clifford algebra and describing its basic properties, we study in detail the quantization map .: ∧(.)→Cl(.) and justify the term “quantiz

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Weil algebras,ng commutative .-differential algebras with connection. As an associative algebra, the Weil algebra is the tensor product of the symmetric algebra and the exterior algebra of .. By considering non-commutative .-differential algebras with connection, we are led to introduce also a non-commutative Wei

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Quantum Weil algebras,y the enveloping algebra . of a Lie algebra is a quantization of the symmetric algebra .. In this chapter we will consider a similar quantization of the Weil algebra ., for any Lie algebra . with a non-degenerate invariant inner product .. For a suitable choice of generators, the quantum Weil algebr

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