Isomorphisms between graded Frobenius algebras constructed from twisted superpotentials

Xuejun Xia; Libin Li

Displaying similar documents to “Isomorphisms between graded Frobenius algebras constructed from twisted superpotentials”

Categorical investigation of $Γ$ -graded $Λ$ -algebras

Huq, S.A., Aijaz, Kulsoom (1969)

Portugaliae mathematica

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Graded morphisms of $G$ -modules

Hanspeter Kraft, Claudio Procesi (1987)

Annales de l'institut Fourier

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Let $A$ be finite dimensional $C$ -algebra which is a complete intersection, i.e. $A = C [X_{1}, ..., X_{n}] / (f_{1}, ..., f_{n})$ whith a regular sequences $f_{1}, ..., f_{n}$ . Steve Halperin conjectured that the connected component of the automorphism group of such an algebra $A$ is solvable. We prove this in case $A$ is in addition graded and generated by elements of degree 1.

Deformations of graded algebras.

Jan O. Kleppe (1979)

Mathematica Scandinavica

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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 $A \oplus B : = ⨁_{k, l} (A_{k} \oplus B_{l})$ , endowed with a suitable bracket, which mimics semidirect products on both sides, becomes a graded Lie algebra $A \oplus_{(α, β)} B$ . 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...

$ℤ_{k + l} \times ℤ_{2}$ -graded polynomial identities for $M_{k, l} (E) \otimes E$

Onofrio Mario Di Vincenzo, Vincenzo Nardozza (2002)

Rendiconti del Seminario Matematico della Università di Padova

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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 $ε : 𝒞^{*} (M) \to 𝑘$ induces a morphism of algebras $I : H H^{*} (𝒞^{*} (M); 𝒞^{*} (M)) \to H H^{*} (𝒞^{*} (M); 𝑘)$ . 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...

Hopf algebras and dendriform structures arising from parking functions

Jean-Christophe Novelli, Jean-Yves Thibon (2007)

Fundamenta Mathematicae

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We introduce a graded Hopf algebra based on the set of parking functions (hence of dimension ${(n + 1)}^{n - 1}$ in degree n). This algebra can be embedded into a noncommutative polynomial algebra in infinitely many variables. We determine its structure, and show that it admits natural quotients and subalgebras whose graded components have dimensions respectively given by the Schröder numbers (plane trees), the Catalan numbers, and powers of 3. These smaller algebras are always bialgebras and belong to...

On finite algebras projectively represented by graded complete intersections.

Günter Scheja, Uwe Storch (1993)

Mathematische Zeitschrift

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