Related papers: Splints of classical root systems

We define the notion of a partially additive Kleene algebra, which is a Kleene algebra where the + operation need only be partially defined. These structures formalize a number of examples that cannot be handled directly by Kleene algebras.…

A class of subsets designated as very thin subsets of natural numbers has been studied and seen that theory of convergence may be rediscovered if very thin sets are given to play main role instead of thin or finite sets which removes some…

The coinvariant algebra of a Weyl group plays a fundamental role in several areas of mathematics. The fake degrees are the graded multiplicities of the irreducible modules of a Weyl group in its coinvariant algebra, and they were computed…

For a simple complex Lie algebra of finite rank and classical type, we fix a triangular decomposition and consider the simple Levi subalgebras associated to closed subsets of roots. We study the restriction of global and local Weyl modules…

Let $k$ be an arbitrary field and $d$ a positive integer. For each degenerate symmetric or antisymmetric bilinear form $M$ on $k^{d}$ we determine the structure of the Lie algebra of matrices that preserve $M$, and of the Lie algebra of…

A 2-sphere embedded in the 4-sphere invariant under a circle action is called a branched twist spin. A branched twist spin is constructed from a 1-knot in the 3-sphere and a pair of coprime integers uniquely. In this paper, we study, for…

We study algebraic tangles as fundamental components in knot theory, developing a systematic approach to classify and tabulate prime tangles using a novel canonical representation. The canonical representation enables us to distinguish…

We describe a method for determining a complete set of integrals for a classical Hamiltonian that separates in orthogonal subgroup coordinates. As examples, we use it to determine complete sets of integrals, polynomial in the momenta, for…

In this paper, we study moduli spaces of low dimensional complex Lie superalgebras. We discover a similar pattern for the structure of these moduli spaces as we observed for ordinary Lie algebras, namely, that there is a stratification of…

We introduce a concept of an embedding of a quadratic space in an associative algebra. The general properties of such embeddings are analyzed by linking it to the Clifford algebra. Conversely, there isa simple description of the standard…

The symplectic blob algebra is a physically motivated quotient of the Hecke algebra $H(\tilde{C}_n)$ with a diagram calculus. We find the blocks for the symplectic blob algebra for all specialisations of its parameters over the complex…

The spin-statistics conection is obtained for classical point particles. The connection holds within pseudomechanics, a theory of particle motion that extends classical physics to include anticommuting Grassmann variables, and which…

We study the Nichols algebra of a semisimple Yetter-Drinfeld module and introduce new invariants such as real roots. The crucial ingredient is a `reflection' in the class of such Nichols algebras. We conclude the classifications of…

We give a criterion allowing to verify whether or not two tilted algebras have the same relation-extension (thus correspond to the same cluster-tilted algebra). This criterion is in terms of a combinatorial configuration in the…

We undertake a detailed investigation into the structure of permutations in monotone grid classes whose row-column graphs do not contain components with more than one cycle. Central to this investigation is a new decomposition, called the…

We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…

Complex networks in natural, social, and technological systems generically exhibit an abundance of rich information. Extracting meaningful structural features from data is one of the most challenging tasks in network theory. Many methods…

The super Weyl group of a basic classical Lie superalgebra was introduced and studied in \cite{PS}, which turns out to play an important role for the study of representations of the basic classical Lie superalgebras and algebraic…

For $d\geq 1$, we define semibricks and wide subcategories in the $d$-extended hearts of bounded $t$-structures on a triangulated category. We show that these semibricks are in bijection with finite-length wide subcategories. When the…

Classical Clifford theory studies the decomposition of simple $G$-modules into simple $H$-modules for some normal subgroup $H \triangleleft G$. In this paper we deal with chains of normal subgroups $1 \triangleleft G_1 \triangleleft \cdots…