Using tensor categories, we present new constructions of several the exceptional simple Lie superalgebras with integer Cartan matrix in characteristic $p = 3$ and 5$ from complete classification modular indecomposable their subquotients over algebraically closed fields by Bouarroudj, Grozman, Leites 2009. Specifically, let $\mathbf{\alpha}_p$ denote kernel Frobenius endomorphism on additive gro...

We associate to an arbitrary positive root [Formula: see text] of a complex semisimple finite-dimensional Lie algebra twisting endofunctor the category text]-modules. apply this functor generalized Verma modules in and construct family text]-Gelfand–Tsetlin with finite text]-multiplicities, where is commutative text]-subalgebra universal enveloping generated by Cartan subalgebra Casimir element...

A notion of an algebroid-a generalization of a Lie algebroid structure on a vector bundle is introduced. We show that many objects of the differential calculus on a manifold M associated with the canonical Lie algebroid structure on TM can be obtained in the framework of a general algebroid. Also a compatibility condition which leads, in general, to a concept of a bialgebroid. 0 Introduction. T...

The chains studied in this paper generalize Chern–Moser chains for CR structures. They form a distinguished family of one dimensional submanifolds in manifolds endowed with a parabolic contact structure. Both the parabolic contact structure and the system of chains can be equivalently encoded as Cartan geometries (of different types). The aim of this paper is to study the relation between these...

Given a finite tensor category $\mathcal {C}$ , we prove that modified trace on the ideal of projective objects can be obtained from suitable trivialization Nakayama functor as right -module functor. Using result Costello, this allows us to associate any equipped with such chain complex valued topological conformal field theory, theory. The theory topologically describes trace, Hattori-Stalling...

In this paper, we are concerned with the existence of local isometric embeddings into Euclidean space for analytic Riemannian metrics g , defined on a domain U ? R n which singular in sense that determinant metric tensor is allowed to vanish at an isolated point (say origin). Specifically, show that, under suitable technical assumptions, there exists embedding u from ( ? ? ? ) E 2 + 3 ? 4 / whe...

We construct exceptional field theory for the duality group SL(3)×SL(2). The theory is defined on a space with 8 ‘external’ coordinates and 6 ‘internal’ coordinates in the (3, 2) fundamental representation, leading to a 14-dimensional generalized spacetime. The bosonic theory is uniquely determined by gauge invariance under generalized external and internal diffeomorphisms. The latter invarianc...

The mean stress tensor is essential to investigate the dynamics of granular material. In this paper, we use Hamilton’s principle least action derive averaged discrete assemblies subjected hydraulic force fields, as well rigorous conditions for a proper definition Representative Volume Element (RVE). main goal behind our efforts upscale particle physics into sound systems involving complex inter...