We study the notion of positive and negative complexity of pairs of objects in cluster categories. The first main result shows that the maximal complexity occurring is either one, two or infinite, depending on the representation type of the underlying hereditary algebra. In the second result, we study the bounded derived category of a cluster tilted algebra, and show that the maximal complexity...

We show that the skew-symmetrized product on every Leibniz algebra E can be realized on a reductive complement to a subalgebra in a Lie algebra. As a consequence, we construct a nonassociative multiplication on E which, when E is a Lie algebra, is derived from the integrated adjoint representation. We apply this construction to realize the bracket operations on the sections of Courant algebroid...

We extend the results we obtained in an earlier work [1]. The cocommutative case of ladders is generalized to a full Hopf algebra of (decorated) rooted trees. For Hopf algebra characters with target space of Rota-Baxter type, the Birkhoff decomposition of renormalization theory is derived by using the RotaBaxter double construction, respectively Atkinson’s theorem. We also outline the extension...

We describe the derived Picard groups and two-term silting complexes for quasi-hereditary algebras with two simple modules. also by quivers relations all equivalent to a algebra

We prove an explicit formula for a projection of singular vectors in the Verma module over a rank 2 Kac-Moody Lie algebra onto the universal enveloping algebra of the Heisenberg Lie algebra and of sl2. The formula is derived from a more general but less explicit formula due to Feigin, Fuchs, and Malikov [3]. In the simpler case of A1 the formula was obtained in [4].

In this paper, we consider the singularity category Dsg(modA) and Z-graded Dsg(modZA) for a Gorenstein monomial algebra A. Firstly, positively graded 1-Gorenstein algebra, prove that its admits silting objects. Secondly, A=KQ/I being has tilting As consequence, is triangulated equivalent to derived of hereditary H which finite representation type. Finally, give characterization algebras, descri...

We show that the fermionic matrix model can be realized by W-representation. construct Virasoro constraints with higher algebraic structures, where constraint operators obey Witt algebra and null 3-algebra. The remarkable feature is character expansion of partition function easily derived from such constraints. It a τ-function KP hierarchy. Aristotelian tensor give its Moreover, we analyze red ...

Performance Evaluation Process Algebra (PEPA) is a formal language for performance modelling based on process algebra. It has previously been shown that using the process algebra apparatus compact performance models can be derived which retain the essential behavioural characteristics of the modelled system. However no ee-cient algorithm for this derivation was given. In this paper we present a...

In this paper, first we define the notion of involutive operator on bounded involutive equality algebras and by using it, we introduce a new class of equality algebras that we called it a tense like equality algebra. Then we investigate some properties of tense like equality algebra. For two involutive bounded equality algebras and an equality homomorphism between them, we prove that the tense ...

Let Λ be a basic finite dimensional algebra over an algebraically closed field $\Bbbk $ , and let $\widehat {\Lambda }$ the repetitive of Λ. In this article, we prove that if {V}$ is left -module with dimension then has well-defined versal deformation ring $R(\widehat },\widehat {V})$ which local complete Noetherian commutative -algebra whose residue also isomorphic to . We }, \widehat universa...