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On a generalization of de Rham lemma

Kyoji Saito (1976)

Annales de l'institut Fourier

Let M be a free module over a noetherian ring. For ω 1 , ... , ω k ∈ M , let 𝒜 be the ideal generated by coefficients of ω 1 ∧ ... ∧ ω k . For an element ω ∈ ⋀ p M with p < prof . 𝒜 , if ω ∧ ω 1 ∧ ... ∧ ω k = 0 , there exists η 1 , ... , η k ∈ ⋀ p - 1 M such that ω = ∑ i = 1 k η i ∧ ω i .This is a generalization of a lemma on the division of forms due to de Rham (Comment. Math. Helv., 28 (1954)) and has some applications to the study of singularities.

On some algebraic identities and the exterior product of double forms

Mohammed Larbi Labbi (2013)

Archivum Mathematicum

We use the exterior product of double forms to free from coordinates celebrated classical results of linear algebra about matrices and bilinear forms namely Cayley-Hamilton theorem, Laplace expansion of the determinant, Newton identities and Jacobi’s formula for the determinant. This coordinate free formalism is then used to easily generalize the previous results to higher multilinear forms namely to double forms. In particular, we show that the Cayley-Hamilton theorem once applied to the second...

Produit tensoriel de matrices, homologie cyclique, homologie des algèbres de Lie

Philippe Gaucher (1994)

Annales de l'institut Fourier

On munit, naturellement, d’un surproduit l’algèbre extérieure de l’homologie cyclique d’une k -algèbre commutative A ( k étant un corps de caractéristique zéro) à l’aide du produit de Loday-Quillen. On munit d’un surproduit l’homologie de l’algèbre de Lie du groupe linéaire général de A à l’aide du produit tensoriel de matrices. On montre que l’isomorphisme d’algèbres de Hopf de Loday-Quillen est compatible avec les surproduits définis ci-dessus. On obtient ainsi une interprétation du produit de Loday-Quillen,...

Spinors in braided geometry

Mićo Đurđević, Zbigniew Oziewicz (1996)

Banach Center Publications

Let V be a ℂ-space, σ ∈ E n d ( V ⊗ 2 ) be a pre-braid operator and let F ∈ l i n ( V ⊗ 2 , ℂ ) . This paper offers a sufficient condition on (σ,F) that there exists a Clifford algebra Cl(V,σ,F) as the Chevalley F-dependent deformation of an exterior algebra C l ( V , σ , 0 ) ≡ V ∧ ( σ ) . If σ ≠ σ - 1 and F is non-degenerate then F is not a σ-morphism in σ-braided monoidal category. A spinor representation as a left Cl(V,σ,F)-module is identified with an exterior algebra over F-isotropic ℂ-subspace of V. We give a sufficient condition on braid σ that the spinor representation...

Transgression and Clifford algebras

Rudolf Philippe Rohr (2009)

Annales de l’institut Fourier

Let W be a differential (not necessarily commutative) algebra which carries a free action of a polynomial algebra S P with homogeneous generators p 1 , ⋯ , p r . We show that for W acyclic, the cohomology of the quotient H ( W / < p ...

Weak Polynomial Identities for M1,1(E)

Di Vincenzo, Onofrio, La Scala, Roberto (2001)

Serdica Mathematical Journal

* Partially supported by Universita` di Bari: progetto “Strutture algebriche, geometriche e descrizione degli invarianti ad esse associate”.We compute the cocharacter sequence and generators of the ideal of the weak polynomial identities of the superalgebra M1,1 (E).

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