Related papers: The Magic of Being Exceptional

Here we demonstrate the emergence of Grassmann variables in matrix models based on the exceptional Jordan algebra. The Grassmann algebras are built naturally using the octonion algebra. We argue the appearance of Grassmann variables…

The article associates two fundamental lattice constructions with each regular unital real ordered Banach space (function system). These are used to establish certain results in the theory of operator algebras, specifically relating the…

We give a computer free proof of the Deligne, Cohen and deMan formulas for the dimensions of the irreducible $g$-modules appearing in the tensor powers of $g$, where $g$ ranges over the exceptional complex simple Lie algebras. We give…

We define and study the essential dimension of an algebraic stack. We compute the essential dimension of the stacks Mgn and MgnBar of smooth, or stable, n-pointed curves of genus g. We also prove a general lower bound for the essential…

The problem of possible astrophysical consequences of the existence of exotic differential structures on manifolds is discussed. It is argued that corrections to the curvature of the form of a source like terms should be expected in the…

Dynamical encirclement of an Exceptional Point (EP) and corresponding time-asymmetric mode evolution properties due to breakdown in adiabatic theorem have been a key to range of exotic physical effects in various open atomic, molecular and…

Quantum bits can be isolated to perform useful information-theoretic tasks, even though physical systems are fundamentally described by very high-dimensional operator algebras. This is because qubits can be consistently embedded into…

Let $J_r$ denote a full $r \times r$ Jordan block matrix with eigenvalue $1$ over a field $F$ of characteristic $p$. For positive integers $r$ and $s$ with $r \leq s$, the Jordan canonical form of the $r s \times r s$ matrix $J_{r} \otimes…

In this paper, we study the class of Jordan dialgebras. We develop an approach for reducing problems on dialgebras to the case of ordinary algebras. It is shown that straightforward generalizations of the classical Cohn's, Shirshov's, and…

Higher-order exceptional points (EPs) in non-Hermitian systems showcase diverse physical phenomena but require more parameter space freedom or symmetries. It leads to a challenge for the exploration of high-order EP geometries in…

Graded rings provide a natural algebraic framework for encoding symmetry via decompositions into homogeneous components indexed by a group, together with multiplication rules reflecting the group operation. Among graded rings, strongly…

In this paper, we look at the number of factorizations of a given permutation into star transpositions. In particular, we give a natural explanation of a hidden symmetry, answering a question of I.P. Goulden and D.M. Jackson. We also have a…

In this paper we look into the structure of finite-dimensional graded superalgebras of various types such as associative, Lie and Jordan over an algebraically closed field of characteristic zero.

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact exceptional algebra $E_{7(-25)}$. Our choice of this particular algebra is motivated by the fact…

In this article we prove that the elliptic, hyperbolic and nilpotent (or unipotent) additive (or multiplicative) Jordan components of an endomorphism $X$ (or an isomorphism $g$) of a finite dimensional vector space are given by polynomials…

Exceptional field theory (EFT) gives a geometric underpinning of the U-duality symmetries of M-theory. In this talk I give an overview of the surprisingly rich algebraic structures which naturally appear in the context of EFT. This includes…

There is a well-known construction of a Jordan algebra via a sharped cubic form. We introduce a generalized sharped cubic form and prove that the split spin factor algebra is induced by this construction and satisfies the identity…

The unrestricted T-system is a family of relations in the Grothendieck ring of the category of the finite-dimensional modules of the Yangian or the quantum affine algebra associated with a complex simple Lie algebra. The unrestricted…

Exceptional points of order $n$ (EP$n$s) appear in non-Hermitian systems as points where the eigenvalues and eigenvectors coalesce. They emerge if $2(n-1)$ real constraints are imposed, such that EP2s generically appear in two dimensions…

For a division ring $D$, denote by $\mathcal M_D$ the $D$-ring obtained as the completion of the direct limit $\varinjlim_n M_{2^n}(D)$ with respect to the metric induced by its unique rank function. We prove that, for any ultramatricial…