This study is based on ‘algebraic-analytic’ approach to some non-associative hyper-structures with application to physical systems. This was with a view of understanding the non-associatve algebraic behaviour of: (i) the elementary particle physics (lepton group) which forms an Hv-group (Nezhad et al. 2012), the elementary particles (including the Higgs Boson) originally studied by (Davvaz et al. 2020) and (ii) some dismutation reactions in chemical systems (Davvaz et al. 2012). Non-commutative groupoid (quasigroup and loop) was used to construct polygroupoid (polyquasigroup, polyloop) and examples given. The Kuratowski closure axioms was used for an appropriate closure operator that is nuclear in nature (relative to polygroupoid) to produce a Kuratowski induced topological space and consequently a polygroupoid-topological space. This study introduced and investigated the properties of left (right) nuclei Kuratowski closure operator induced topological space on polygroupoid (polyquasigroup, polyloop). This was used to analyse (with the aid of probability) the nuclear and alternative properties of the lepton group. The analysis of algebraic properties (with the aid of probability of elements) in dismutation reaction of some chemical systems of Tin (Sn), Indium (In) and Vanadium (V) which are represented by hyper-algebraic structures were carried out.
A study of non-associative hyper-structures and algebraic analysis of selected physical systems
Tue, Apr. 15 2:30pm (MATH 3…
Lie Theory
Gurbir Dhillon (UCLA)
X
The representation theory of affine Lie algebras in characteristic zero has been well studied for over fifty years, and has rich connections with algebraic geometry, mathematical physics, and number theory. By contrast, in positive characteristic, much less is known. In the talk, I will review some earlier results in this area, and state some new ones, namely the determination of the Harish--Chandra center and the linkage principle for highest weight representations at all levels. Time permitting, we will discuss some further conjectures. This is based on joint work in progress with Ivan Loseu.
Representations of affine Lie algebras in positive characteristic
The (classical) Adams spectral sequence was one of the first major computational tools developed in stable homotopy theory. In this talk we will give an overview of the construction of the spectral sequence and, time permitting, perform some low-dimensional computations.
A study of non-associative hyper-structures and algebraic analysis of selected physical systems