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Displaying similar documents to “Graded morphisms of G -modules”

Isomorphisms between graded Frobenius algebras constructed from twisted superpotentials

Xuejun Xia, Libin Li (2022)

Czechoslovak Mathematical Journal

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In order to distinguish the connected graded Frobenius algebras determined by different twisted superpotentials, we introduce the nondegeneracy of twisted superpotentials. We give the sufficient and necessary condition for connected graded Frobenius algebras determined by two nondegenerate twisted superpotentials to be isomorphic. As an application, we classify the connected ℤ -graded Frobenius algebra of length 3, whose dimension of the degree 1 is 2.

Equivariant deformation quantization for the cotangent bundle of a flag manifold

Ranee Brylinski (2002)

Annales de l’institut Fourier

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Let X be a (generalized) flag manifold of a complex semisimple Lie group G . We investigate the problem of constructing a graded star product on ℛ = R ( T ☆ X ) which corresponds to a G -equivariant quantization of symbols into twisted differential operators acting on half-forms on X . We construct, when ℛ is generated by the momentum functions μ x for G , a preferred choice of ☆ where μ x ☆ φ has the form μ x φ + 1 2 { μ x , φ } t + Λ x ( φ ) t 2 . Here Λ x are operators on ℛ . In the known examples, Λ x ( x ≠ 0 ) is not a differential operator, and so the star...

The Hochschild cohomology of a closed manifold

Yves Felix, Jean-Claude Thomas, Micheline Vigué-Poirrier (2004)

Publications Mathématiques de l'IHÉS

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Let M be a closed orientable manifold of dimension and 𝒞 * ( M ) be the usual cochain algebra on M with coefficients in a field. The Hochschild cohomology of M, H H * ( 𝒞 * ( M ) ; 𝒞 * ( M ) ) is a graded commutative and associative algebra. The augmentation map ε : 𝒞 * ( M ) → 𝑘 induces a morphism of algebras I : H H * ( 𝒞 * ( M ) ; 𝒞 * ( M ) ) → H H * ( 𝒞 * ( M ) ; 𝑘 ) . In this paper we produce a chain model for the morphism I. We show that the kernel of I is a nilpotent ideal and that the image of I is contained in the center of H H * ( 𝒞 * ( M ) ; 𝑘 ) , which is in general quite small. The algebra H H * ( 𝒞 * ( M ) ; 𝒞 * ( M ) ) is expected to...

Knit products of graded Lie algebras and groups

Michor, Peter W.

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Let A = ⨁ k A k and B = ⨁ k B k be graded Lie algebras whose grading is in 𝒵 or 𝒵 2 , but only one of them. Suppose that ( α , β ) is a derivatively knitted pair of representations for ( A , B ) , i.e. α and β satisfy equations which look “derivatively knitted"; then A ⊕ B : = ⨁ k , l ( A k ⊕ B l ) , endowed with a suitable bracket, which mimics semidirect products on both sides, becomes a graded Lie algebra A ⊕ ( α , β ) B . This graded Lie algebra is called the knit product of A and B . The author investigates the general situation for any graded Lie subalgebras A and...