Related papers: Polygroupoid, Polyquasigroup, Polyloop and their N…
These summer school lectures cover the use of algebraic techniques in various subfields of nuclear physics. After a brief description of groups and algebras, concepts of dynamical symmetry, dynamical supersymmetry, and supersymmetric…
The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…
We introduce several algebraic structures related to handlebody-knots, including $G$-families of biquandles, partially multiplicative biquandles and group decomposable biquandles. These structures can be used to color the semiarcs in…
In this paper, we have studied the loops which are the semidirect products of a loop and a group. Also, the cummutant, nuclei and the center of such loops are studied.
We approach Mackenzie's LA-groupoids from a supergeometric point of view by introducing Q-groupoids, which are groupoid objects in the category of Q-manifolds. There is a faithful functor from the category of LA-groupoids to the category of…
The theory of composite mixtures consisting of $n$ constituents is framed within the schema provided by the notion of $n$-groupoid. The point of departure is the analysis of $n$-dimensional hypercubes and their skeletons, to each of whose…
Several topics concerning nuclear structure and electromagnetic interactions of heavy nuclei are reviewed. These comprehend the deformed single-particle shell model, nuclear collective motion, symmetry breaking and approximate symmetry…
The Poisson structures on two-dimensional Galilei group, classified in the author previous paper are quantized. The dual quantum Galilei Lie algebras are found.
There exists just one regular polytope of rank larger than 3 whose full automorphism group is a projective general linear group PGL_2(q), for some prime-power q. This polytope is the 4-simplex and the corresponding group is PGL_2(5), which…
In the present paper we define homogeneous algebraic systems. Particular cases of these systems are: semigroup (monoid, group) system. These algebraic systems were studied by J. Loday, A. Zhuchok, T. Pirashvili, N. Koreshkov. Quandle…
Consider the smooth quadric Q_6 in P^7. The middle homology group H_6(Q_6,Z) is two-dimensional with a basis given by two classes of linear subspaces. We classify all threefolds of bidegree (1,p) inside Q_6.
We give an elementary introduction to the structure of supergravity theories. This leads to a table with an overview of supergravity and supersymmetry theories in dimensions 4 to 11. The basic steps in constructing supergravity theories are…
Inspired by Coxeter's notion of Petrie polygon for $d$-polytopes (see \cite{Cox73}), we consider a generalization of the notion of zigzag circuits on complexes and compute the zigzag structure for several interesting families of…
In this paper, the module algebra structures of $X_{q}(A_{1})$ on quantum polynomial algebra $\C_{q}[x,y,z]$ are investigated, and a complete classification of $X_{q}(A_{1})$-module algebra structures on $\C_{q}[x,y,z]$ is given
Energy levels of the double-$\Lambda$ hypernuclei $_\Lambda^{}$$_\Lambda^7$He, $_\Lambda^{}$$_\Lambda^7$Li, $_\Lambda^{}$$_\Lambda^8$Li, $_\Lambda^{}$$_\Lambda^9$Li, $_\Lambda^{}$$_\Lambda^9$Be and $_\Lambda^{}$$_\Lambda^{10}$Be are…
This paper gives an introduction to some results on monodromy groupoids and the monodromy principle, and then develops the notion of monodromy groupoid for group groupoids.
More than half a century after the fundamental, spherical shell structure in nuclei has been established, theoretical predictions indicate that the shell-gaps comparable or even stronger than those at spherical shapes may exist.…
In this paper, we introduce right-invariant (similarly, left-invariant) Poisson-Nijenhuis Structures on Lie groupoids and their infinitesimal counterparts as called $(\Lambda , \mathbf{n})-$structures. We present a mutual correspondence…
We constuct a family of hemisystems of the parabolic quadric $\mathcal{Q}(2d, q)$, for all ranks $d \ge 2$ and all odd prime powers $q$, that admit $\Omega_3(q) \cong \mathrm{PSL}_2(q)$. This yields the first known construction for $d \ge…
In this contribution, I discuss the role of symmetries and algebraic methods in nuclear structure physics. In particular, I review some recent developments in nuclear supersymmetry and indicate possible applications for light nuclei in the…