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Isomorphisms between graded Frobenius algebras constructed from twisted superpotentials

Xuejun Xia, Libin Li (2022)

Czechoslovak Mathematical Journal

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 -graded Frobenius algebra of length 3, whose dimension of the degree 1 is 2.

Jordan superderivations and Jordan triple superderivations of superalgebras

He Yuan, Liangyun Chen (2016)

Colloquium Mathematicae

We study Jordan (θ,θ)-superderivations and Jordan triple (θ,θ)-superderivations of superalgebras, using the theory of functional identities in superalgebras. As a consequence, we prove that if A = A₀ ⊕ A₁ is a prime superalgebra with deg(A₁) ≥ 9, then Jordan superderivations and Jordan triple superderivations of A are superderivations of A, and generalized Jordan superderivations and generalized Jordan triple superderivations of A are generalized superderivations of A.

Local superderivations on Lie superalgebra 𝔮 ( n )

Haixian Chen, Ying Wang (2018)

Czechoslovak Mathematical Journal

Let 𝔮 ( n ) be a simple strange Lie superalgebra over the complex field . In a paper by A. Ayupov, K. Kudaybergenov (2016), the authors studied the local derivations on semi-simple Lie algebras over and showed the difference between the properties of local derivations on semi-simple and nilpotent Lie algebras. We know that Lie superalgebras are a generalization of Lie algebras and the properties of some Lie superalgebras are similar to those of semi-simple Lie algebras, but 𝔭 ( n ) is an exception. In this...

On the classification of 3-dimensional coloured Lie algebras

Sergei Silvestrov (1997)

Banach Center Publications

In this paper, complex 3-dimensional Γ-graded ε-skew-symmetric and complex 3-dimensional Γ-graded ε-Lie algebras with either 1-dimensional or zero homogeneous components are classified up to isomorphism.

The ℤ₂-graded sticky shuffle product Hopf algebra

Robin L. Hudson (2006)

Banach Center Publications

By abstracting the multiplication rule for ℤ₂-graded quantum stochastic integrals, we construct a ℤ₂-graded version of the Itô Hopf algebra, based on the space of tensors over a ℤ₂-graded associative algebra. Grouplike elements of the corresponding algebra of formal power series are characterised.

Uniqueness of decomposition of pseudo-Riemannian superalgebras

Keli Zheng, Liangyun Chen, Yongzheng Zhang (2014)

Colloquium Mathematicae

This paper is primarily concerned with pseudo-Riemannian superalgebras, which are superalgebras endowed with pseudo-Riemannian non-degenerate supersymmetric consistent bilinear forms. Decompositions of pseudo-Riemannian superalgebras whose left centers are isotropic and whose left centers are not isotropic are investigated.

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).

Z2-Graded Polynomial Identities for Superalgebras of Block-Triangular Matrices

Di Vincenzo, Onofrio (2004)

Serdica Mathematical Journal

000 Mathematics Subject Classification: Primary 16R50, Secondary 16W55.We present some results about the Z2-graded polynomial identities of block-triangular matrix superalgebras R[[A M],[0 B]]. In particular, we describe conditions for the T2-ideal of a such superalgebra to be factorable as the product T2(A)T2(B). Moreover, we give formulas for computing the sequence of the graded cocharacters of R in some interesting case.Partially supported by MURST COFIN 2003 and Università di Bari.

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