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Dialgebras are generalizations of associative algebras which give rise to Leibniz algebras instead of Lie algebras. In this paper we study super dialgebras and Leibniz superalgebras, which are $\z_2$-graded dialgebras and Leibniz algebras.…
We consider the natural Lie algebra structure on the (associative) group algebra of a finite group $G$, and show that the Lie subalgebras associated to natural involutive antiautomorphisms of this group algebra are reductive ones. We give a…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
Recently, a new generalized family of infinite-dimensional $ \widetilde{W} $ algebras, each associated with a particular element of a commutative subalgebra of the $ W_{1+\infty} $ algebra, was described. This paper provides a comprehensive…
Aperiodic algebras are infinite dimensional algebras with generators corresponding to an element of the aperiodic set. These algebras proved to be an useful tool in studying elementary excitations that can propagate in multilayered…
There is a growing interest in the logical possibility that exceptional mathematical structures (exceptional Lie and superLie algebras, the exceptional Jordan algebra, etc.) could be linked to an ultimate "exceptional" formulation for a…
There has recently been interest in relating properties of matrices drawn at random from the classical compact groups to statistical characteristics of number-theoretical L-functions. One example is the relationship conjectured to hold…
We study locally finite varieties (=primitive classes) of linear algebras over finite fields. We do not assume that our algebras are associative or Lie. We are interested in the basic properties of finite algebras in these varieties such…
Superderivations for the eight families of finite or infinite dimensional graded Lie superalgebras of Cartan-type over a field of characteristic $p>3$ are completely determined by a uniform approach: The infinite dimensional case is reduced…
The graded Lie algebra associated with the Nottingham group over a field of prime characteristic serves as a fundamental example of Nottingham algebras, a class of infinite-dimensional, positively graded thin algebras. This paper completes…
For sufficiently high dimensions, the naturally graded nonsplit nilpotent Lie algebras with linear characteristic sequence are classified.
Let $g$ be an affine Lie algebra with index set $I = \{0, 1, 2,..., n\}$ and $g^L$ be its Langlands dual. It is conjectured that for each $i \in I \setminus \{0\}$ the affine Lie algebra $g$ has a positive geometric crystal whose…
The structure of Lie algebras, Lie superalgebras and Leibniz algebras graded by finite root systems has been studied by several researchers since 1992. In this paper, we study the structure of Leibniz superalgebras graded by finite root…
The aim of this paper is to extend the structure theory for infinitely generated modules over tame hereditary algebras to the more general case of modules over concealed canonical algebras. Using tilting, we may assume that we deal with…
To an $r$-dimensional subshift of finite type satisfying certain special properties we associate a $C^*$-algebra $\cA$. This algebra is a higher rank version of a Cuntz-Krieger algebra. In particular, it is simple, purely infinite and…
Exceptional sequences are fundamental to investigate the derived categories of finite dimensional algebras. The aim of this note is to classify all the complete exceptional sequences over the path algebra of a Dynkin quiver of type $A_n$ in…
In this paper we study the lengths of certain chains of subalgebras of a Lie algebra L: namely, a chief series, a maximal chain of minimal length, a chain of maximal length in which each subalgebra is modular in L, and a chain of maximal…
Algebras of Logic deal with some algebraic structures, often bounded lattices, considered as models of certain logics, including logic as a domain of order theory. There are well known their importance and applications in social life to…
The description of irreducible finite dimensional representations of finite dimensional solvable Lie superalgebras over complex numbers given by V.~Kac is refined. In reality these representations are not just induced from a polarization…
The goal of this paper is to explicitly describe in terms of generators and relations the universal central extension of the infinite dimensional Lie algebra, $\mathfrak{g} \otimes \mathbb{C}[t,t^{-1},u]$ with finite dimensional simple Lie…