Related papers: Noncommutative Symmetric Systems over Associative …

Non-Hermitian disordered systems have emerged as a central arena in modern physics, with ramifications spanning condensed matter, quantum, statistical, and high energy contexts. The same principles also underlie phenomena beyond physics,…

We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and the ring of symmetric functions in…

The structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group is related to a notion of Hilbert modules endowed with inner products taking values in spaces of unbounded operators. A…

We present a method for computing the Hilbert series of the algebra of invariants of the complex symplectic and orthogonal groups acting on graded noncommutative algebras with homogeneous components which are polynomial modules of the…

A Hopf algebra with four generators among which an involution (reflection) operator, is introduced. The defining relations involve commutators and anticommutators. The discrete series representations are developed. Designated by…

We study Van den Bergh's noncommutative symmetric algebra $\mathbb{S}^{nc}(M)$ (over division rings) via Minamoto's theory of Fano algebras. In particular, we show $\mathbb{S}^{nc}(M)$ is coherent, and its proj category $\mathbb{P}^{nc}(M)$…

Superconducting cosmic strings (SCSs) have received revived interests recently. In this paper we treat closed SCSs as oriented knotted line defects, and concentrate on their topology by studying the Hopf topological invariant. This…

Hopf algebraic structures will replace groups and group representations as the leading paradigm in forthcoming times. K-theory, co-homology, entanglement, statistics, representation categories, quantized or twisted structures as well as…

We study theories with W-algebra symmetries and their relation to WZNW models on (super-)groups. Correlation functions of the WZNW models are expressed in terms of correlators of CFTs with W-algebra symmetry. The symmetries of the theories…

We give new examples of noncommutative manifolds that are less standard than the NC-torus or Moyal deformations of $\Rb^n$. They arise naturally from basic considerations of noncommutative differential topology and have non-trivial global…

We develop a framework for constructing superconformal blocks for correlators of general supermultiplets in theories with $\mathrm{SU}(m,m|2n)$ symmetry, such as four-dimensional $\mathcal{N}=2$ and $\mathcal{N} = 4$ conformal theories. We…

We consider graded representations of the algebra NC of noncommutative symmetric functions on the Z-linear span of a graded poset P. The matrix coefficients of such a representation give a Hopf morphism from a Hopf algebra HP generated by…

Let $\fS$ be an analytic free semigroup algebra. In this paper, we explore richer structures of $\fS$ and its predual $\fS_*$. We prove that $\fS$ and $\fS_*$ both are Hopf algebras. Moreover, the structures of $\fS$ and $\fS_*$ are closely…

We identify the quantum isometry groups of spectral triples built on the symmetric groups with length functions arising from the nearest-neighbor transpositions as generators. It turns out that they are isomorphic to certain "doubling" of…

We study noncommutative differential structures on the group of permutations $S_N$, defined by conjugacy classes. The 2-cycles class defines an exterior algebra $\Lambda_N$ which is a super analogue of the Fomin-Kirillov algebra $\CE_N$ for…

A super-algebraic formulation of the N=2 supersymmetric unconstrained matrix (k|n,m)-MGNLS hierarchies (nlin.SI/0201026) is established. Recursion operators, fermionic and bosonic symmetries as well as their superalgebra are constructed for…

In this paper, we study non-adjacent BCFW recursion relations and their connection to positive geometry. For an adjacent BCFW shift, the $n$-point N$^k$MHV tree-level amplitude in ${\cal N}=4$ SYM theory is expressed as a sum over planar…

A Chen generating series, along a path and with respect to $m$ differential forms,is a noncommutative series on $m$ letters and with coefficients which are holomorphic functionsover a simply connected manifold in other words a series with…

A generalized non-Hermitian oscillator Hamiltonian is proposed that consists of additional linear terms which break PT-symmetry explicitly. The model is put into an equivalent Hermitian form by means of a similarity transformation and the…

Let $(W,S)$ be a finite Coxeter system. Tits defined an associative product on the set $\Sigma$ of simplices of the associated Coxeter complex. The corresponding semigroup algebra is the Solomon-Tits algebra of $W$. It contains the Solomon…