Related papers: Birman-Ko-Lee Left Canonical Form and its Applicat…
We introduce a new cohomology for Lie algebroids, and prove that it provides a differential graded Lie algebra which ``controls'' deformations of the structure bracket of the algebroid. We also have a closer look at various special cases…
Taking the Levine-Tristram signature of the closure of a braid defines a map from the braid group to the integers. A formula of Gambaudo and Ghys provides an evaluation of the homomorphism defect of this map in terms of the Burau…
The first aim of this paper is to introduce and study symmetric (Bi)Hom-Leibniz algebras, which are left and right Leibniz algebras. We discuss $\alpha^k\beta^l$-generalized derivations, $\alpha^k\beta^l$ -quasi-derivations and…
A method to obtain explicit and complete topological solution of SU(2) Chern-Simons theory on $S^3$ is developed. To this effect the necessary aspects of the theory of coloured-oriented braids and duality properties of conformal blocks for…
The decomposition of a quasi-abelian code into shorter linear codes over larger alphabets was given in (Jitman, Ling, (2015)), extending the analogous Chinese remainder decomposition of quasi-cyclic codes (Ling, Sol\'e, (2001)). We give a…
We consider the Hurwitz action on quasipositive factorizations of 3-braids. We prove that every orbit contains an element of a special form. This fact provides an algorithm of finding representatives of every orbit for a given braid. We…
We obtain new presentations for the imprimitive complex reflection groups of type $(de,e,r)$ and their braid groups $B(de,e,r)$ for $d,r \ge 2$. Diagrams for these presentations are proposed. The presentations have much in common with…
The group described in this paper appeared while studying fundamental groups of complements of branch curves. It turned out that a certain quotient of the braid group acts on those fundamental groups and studying this action is essential…
To a Hodge structure V of weight k with CM by a field K we associate Hodge structures V_{-n/2} of weight k+n for n positive and, under certain circumstances, also for n negative. We show that these `half twists' come up naturally in the…
A general method based on the polynomial deformations of the Lie algebra sl(2,R) is proposed in order to exhibit the quasi-exactly solvability of specific Hamiltonians implied by quantum physical models. This method using the…
We apply the technique of twisted extensions of infinite-dimensional Lie algebras to find new 3D integrable {\sc pde}s related to the deformations of Lie algebra $\mathbb{R}_N[s]\otimes \mathfrak{w}$ with $N=1, 2$ as well as to the Lie…
We introduce a new point of view to present classical notions related to set-theoretic solutions of the Yang-Baxter equation: left skew braces, dirings, left skew rings. The idea is to replace the single multiplication on a left near-ring…
We prove a result on linear forms related to Peres-Schlag's theorem on badly approximable numbers with respect to lacunary sequences.
A deformed $q$-calculus is developed on the basis of an algebraic structure involving graded brackets. A number operator and left and right shift operators are constructed for this algebra, and the whole structure is related to the algebra…
We survey geometric quantization of finite dimensional affine Kahler manifolds. Its corresponding prequantization and the Berezin's deformation quantization formulation, as proposed by Cahen et al., is used to quantize their corresponding…
In this work, we show that along a particular choice of Hermitian curvature flow, the non-positivity of Chern-Ricci curvature will be preserved if the initial metric has non-positive bisectional curvature. As an application, we show that…
We use Ozsv\'ath, Stipsicz, and Szab\'o's Upsilon-invariant to provide bounds on cobordisms between knots that `contain full-twists'. In particular, we recover and generalize a classical consequence of the Morton-Franks-Williams inequality…
Quantum sinh-Gordon model in 1+1 dimensions is one of the simplest and best-studied massive integrable relativistic quantum field theories. We consider this theory on a multi-sheeted Riemann surfaces with a flat metric, which can be seen as…
Let $(G,g)$ be a 4-dimensional Riemannian Lie group with a 2-dimensional left-invariant, conformal foliation $\F$ with minimal leaves. Let $J$ be an almost Hermitian structure on $G$ adapted to the foliation $\F$. We classify such…
In this paper, we consider compatible Hom-Lie algebras as a twisted version of compatible Lie algebras. Compatible Hom-Lie algebras are characterized as Maurer-Cartan elements in a suitable bidifferential graded Lie algebra. We also define…