We investigate the ε-Lie structure of K and K,K; here K denotes the skew-symmetric elements of an (ε,G)-Lie color algebra (obtained from an associated algebra A) with an ε-involution. The ...relationship with the (associative) ideals of A is also explored.
The classification of irreducible unital commutative power-associative modules for Hn(F), the algebra of symmetric matrices with the Jordan product, over a field F of characteristic not 2, 3 and 5 ...are given, for n≥3. It is proved that there exists, up to isomorphisms, only one irreducible module which is not Jordan. It is also shown that every finite dimensional unital commutative power associative module for this algebra is completely reducible.
Let V be a vertex operator superalgebra and G a finite automorphism group of V. Let σ be the order 2 automorphism of V associated with the superstructure of V. A sequence of associative algebras ...AG,n(V) are constructed to study the twisted representations of V for nonnegative n∈1T′Z where T′ is the order of group generated by G and σ. This result which generalizes many previous results on Zhu's algebras is then used to investigate the super orbifold theory. If V is a simple vertex operator superalgebra and S is a finite set of inequivalent irreducible twisted V-modules which is closed under the action of G, a duality theorem of Schur-Weyl type is obtained for the actions of certain finite dimensional semisimple associated algebra Aα(G,S) and VG on the direct sum of twisted V-modules in S. In particular, for any g∈G every irreducible g-twisted V-module is completely reducible VG-module.
In this paper we discuss finite presentability of the universal central extensions of Lie algebras sln(R), where n≥3 and R is a unital associative k-algebra. We show that a universal central ...extension is finitely presented if and only if the algebra R is finitely presented.
We introduce the notion of length for non-associative finite-dimensional unitary algebras and obtain a sharp upper bound for the lengths of algebras belonging to this class. We also put forward a new ...method of characteristic sequences based on linear algebra technique, which provides an efficient tool for computing the length function in non-associative case. Then we apply the introduced method to obtain an upper bound for the length of an arbitrary locally complex algebra. In the last case the length is bounded in terms of the Fibonacci sequence. We present concrete examples demonstrating the sharpness of our bounds.
We extend the theory of Matsuo algebras, which are certain non-associative algebras related to 3-transposition groups, to characteristic 2. The decompositions of our algebras are now induced by ...nilpotent elements associated to lines in the corresponding Fischer space, rather than idempotent elements associated to points. For many 3-transposition groups, this still gives rise to a Z/2Z-graded fusion law, and we provide a complete classification of when this occurs. In one particular small case, arising from the 3-transposition group Sym(4), the fusion law is even stronger, and the resulting Miyamoto group is an algebraic group Ga2⋊Gm.
We consider the quantization procedure and investigate the application of the quantizer–dequantizer method and star-product technique to construct associative products and the associative algebras ...formed by the quantizer–dequantizer operators and their symbols. The corresponding Lie algebras are also constructed. We study the case where the quantizer–dequantizer operators form a self-dual system and show that the structure constants of the Lie algebras satisfy some identity, in addition to the Jacobi identity. Using tomographic quantizer–dequantizer operators and their symbols, we construct the continuous associative algebra and the corresponding Lie algebra.
•The quantization procedure, the quantizer-dequantizer method, and star-product technique are considered to construct associative products and the associative algebras formed by the quantizer-dequantizer operators and their symbols.•The corresponding Lie algebras are constructed, and the case where the quantizer-dequantizer operators form a self-dual system is considered.•Using tomographic quantizer-dequantizer operators and their symbols, the continuous associative algebra and the corresponding Lie algebra are constructed.
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