Related papers: Representations of abstract copolarity one and two
We find a spinorial representation of a Riemannian or Lorentzian surface in a Lorentzian homogeneous space of dimension $3.$ We in particular obtain a representation theorem for surfaces in the $\mathbb{L}(\kappa,\tau)$ spaces. We then…
In this paper, we introduce and study representation homology of topological spaces, which is a natural homological extension of representation varieties of fundamental groups. We give an elementary construction of representation homology…
The theorem of orthogonal-orthogonal duality of Rowe, Repka, and Carvalho is proven by a method based on characters that is very different from theirs and akin to Helmers's half a century earlier proof of the analogous sympletic-symplectic…
It is a well-known fact that endomorphisms of $B(H)$ are intimately connected with families of mutually orthogonal isometries, i.e. with representations of the so-called Toeplitz $C^*$-algebras. In this paper we consider a natural…
Real forms of a complex reductive group are classified by Galois cohomology H^1(Gamma,G_ad) where G_ad is the adjoint group. Cartan's classification of real forms in terms of maximal compact subgroups can be stated in terms of H^(Z/2Z,G_ad)…
We examine the Hochschild cohomology for triangular algebras that capture some aspects of geometry and topology of the torus and of the quadric surface, and for deformations of these algebras. In particular, this shows that the cup product…
This reply tries to rectify some misunderstandings that are in our opinion contained in the Comment by Campostrini and Rossi, <hep-lat 99407008> on our paper <hep-lat 9407003>.
In this paper we determine the second Hochschild cohomology group for a class of self-injective algebras of tame representation type namely, those which are standard one-parametric but not weakly symmetric. These were classifed up to…
Interrelation of the Coleman's representabilty theory for 1-density operators and abstract algebraic form of the Hohenberg-Kohn theorem is studied in detail. Convenient realization of the Hohenberg-Kohn set of classes of 1-electron…
We introduce and characterize a particularly tractable class of unital type 1 C*-algebras with bounded dimension of irreducible representations. Algebras in this class are called recursive subhomogeneous algebras, and they have an inductive…
Bihom-Lie algebra is a generalized Hom-Lie algebra endowed with two commuting multiplicative linear maps. In this paper, we study cohomology and representations of Bihom-Lie algebras. In particular, derivations, central extensions,…
In this paper, we introduce cohomology of n-Hom-Liebniz algebra morphisms and formal deformation theory of n-Hom-Liebniz algebra morphisms .
We study in detail the one-variable local theory of functions holomorphic over a finite-dimensional commutative associative unital $\mathbb{C}$-algebra $\mathcal{A}$, showing that it shares a multitude of features with the classical…
The main purpose of this paper is to provide a second cohomology group of a (metric) Hom-Jacobi algebra with coefficients in a given representation. Moreover, we show that second cohomology group classifies abelian extensions of a (metric)…
The purpose of this paper is to study deformation theory of Hom-associative algebra morphisms and Hom-Lie algebra morphisms. We introduce a suitable cohomology and discuss Infinitesimal deformations, equivalent deformations and…
Recently, an infinite class of holographic generalized complexities was proposed. These gravitational observables display the behavior required to be duals of complexity, in particular, linear growth at late times and switchback effect. In…
We discuss two possible ways of representing tolerances: first, as a homomorphic image of some congruence; second, as the relational composition of some compatible relation with its converse. The second way is independent from the variety…
Angular parts of certain solvable models are studied. We find that an extension of this class may be based on suitable trigonometric identities. The new exactly solvable Hamiltonians are shown to describe interesting two- and three-particle…
Two new notions of equivalence for representations of a Toeplitz algebra $\mathcal{E}_n$, $n<\infty$, on a common Hilbert space are defined. Our main results apply to $C^*$-dynamics and the conjugacy of certain $*$-endomorphisms. One…
This paper deals with the variety of commutative algebras satisfying one of the four families of degree four identities found by Carini, Hentzel and Piacentini-Cattaneo in 1988. We give a characterization of representations and irreducible…