In connection with the work of Malev published in [J. Algebra Appl.13 (2014) 1450004; J. Algebra Appl.20 (2021) 2150074], we continue to provide a classification of possible images of multilinear polynomials on generalized quaternion algebras.
In connection with the work of Malev published in [J. Algebra Appl.13 (2014) 1450004; J. Algebra Appl.20 (2021) 2150074], we continue to provide a classification of possible images of multilinear polynomials on generalized quaternion algebras.
For a pre-Lie–Yamaguti algebra , by using its sub-adjacent Lie–Yamaguti algebra , we are able to construct a semidirect product Lie–Yamaguti algebra via a representation of . The investigation of such semidirect Lie–Yamaguti algebras leads us to the notions of para-Kähler structures and pseudo-Kähler structures on Lie–Yamaguti algebras, and also gives the definition of complex product structures on Lie–Yamaguti algebras. Furthermore, a Levi–Civita product with respect to a pseudo-Riemannian Lie–Yamaguti algebra is introduced and we explore its relation with pre-Lie–Yamaguti algebras.
Let be a finite -group. Then is said to be a -group if for every nonnormal subgroup of . In this paper, we study the -group and get . It is proved that if and if .
We introduce the concepts of relative (strongly) cotorsion and relative Gorenstein cotorsion modules for a non-necessarily semidualizing module and prove that there exists a unique hereditary abelian model structure where the cofibrations are the monomorphisms with relative Gorenstein flat cokernel and the fibrations are the epimorphisms with relative cotorsion kernel belonging to the Bass class. In the particular case of a semidualizing module, we investigate the existence of abelian model structures on the category of left (right) R-modules where the cofibrations are the epimorphisms (monomorphisms) with kernel (cokernel) belonging to the Bass (Auslander) class. We also show that the class of relative Gorenstein flat modules and the Bass class are part of weak AB-contexts.
In this paper, the norm of the lower central series in a finite group is introduced, which unifies the norm of derived subgroups and nilpotent residuals. Some propositions of are obtained, and some related subgroups as well as their equivalent propositions can also be found.
The axioms of a quandle imply that the columns of its Cayley table are permutations. This paper studies quandles with exactly one non-trivially permuted column. Their automorphism groups, quandle polynomials, (symmetric) cohomology groups, and quandles are studied. The quiver and cocycle invariant of links using these quandles are shown to relate to linking number.
In this paper, we construct a differential graded Lie algebra whose Maurer–Cartan elements are given by crossed homomorphisms on Leibniz algebras. This allows us to define cohomology for a crossed homomorphism. Finally, we study linear deformations, formal deformations and extendibility of finite order deformations of a crossed homomorphism in terms of the cohomology theory.
The Morita equivalences of classical Brauer algebras and classical Birman–Murakami–Wenzl (BMW) algebras have been well studied. Here, we study the Morita equivalence problems on these two kinds of algebras of simply-laced type, especially for them with the generic parameters. We show that Brauer algebras and BMW algebras of simply-laced type are Morita equivalent to the direct sums of some group algebras of Coxeter groups and some Hecke algebras of Coxeter groups, respectively.
Let be a simply connected and simple algebraic group defined and split over a finite prime field of elements. In this paper, using an -linear map splitting Frobenius endomorphism on a hyperalgebra relative to , we obtain some -linear isomorphisms induced by multiplication in the hyperalgebra.
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