Let n≥2 be a fixed integer and A be a Csup.∗-algebra. A permuting n-linear map G:Asup.n→A is known to be symmetric generalized n-derivation if there exists a symmetric n-derivation D:Asup.n→A such ...that G(ςsub.1,ςsub.2,…,ςsub.iςsub.i sup.′,…,ςsub.n)=G(ςsub.1,ςsub.2,…,ςsub.i,…,ςsub.n)ςsub.i sup.′+ςsub.iD(ςsub.1,ςsub.2,…,ςsub.i sup.′,…,ςsub.n) holds ∀ςsub.i,ςsub.i sup.′∈A. In this paper, we investigate the structure of Csup.∗-algebras involving generalized linear n-derivations. Moreover, we describe the forms of traces of linear n-derivations satisfying certain functional identity.
In this paper we study the class of laterally complete commutative unital regular algebras A over arbitrary fields. We introduce a notion of passport GAMMA(X) for a faithful regular laterally ...complete A-modules X, which consist of uniquely defined partition of unity in the Boolean algebra of all idempotents in A and of the set of pairwise different cardinal numbers. We prove that A-modules X and Y are isomorphic if and only if GAMMA(X) = GAMMA(Y). Further we study Banach A-modules in the case A = C.sub.infinity(Q) or A = C.sub.infinity(Q)+i*C.sub.infinity(Q). We establish the equivalence of all norms in a finite-dimensional (respectively, sigma-finite-dimensional) A-module and prove an Aversion of Riesz Theorem, which gives the criterion of a finite-dimensionality (respectively, sigma-finite-dimensionality) of a Banach A-module.
Character measure is a probability measure on irreducible representations of a semisimple Lie algebra. It appears from the decomposition into irreducibles of tensor power of a fundamental ...representation. In this paper we calculate the asymptotics of character measure on representations of so.sub.2n+1 in the regime near the boundary of weight diagram. We find out that it converges to a Poisson-type distribution. Bibliography: 8 titles.
In this manuscript, we proposed a novel framework of the q-rung orthopair fuzzy subfield (q-ROFSF) and illustrate that every Pythagorean fuzzy subfield is a q-rung orthopair fuzzy subfield of a ...certain field. We extend this theory and discuss its diverse basic algebraic characteristics in detail. Furthermore, we prove some fundamental results and establish helpful examples related to them. Moreover, we present the homomorphic images and pre-images of the q-rung orthopair fuzzy subfield (q-ROFSF) under field homomorphism. We provide a novel ideology of a non-standard fuzzy subfield in the extension of the q-rung orthopair fuzzy subfield (q-ROFSF).
Abstract
We discuss how one can systematically construct point particle theories that realize the vanishing one-loop cosmological constant without Bose–Fermi cancellation. Our construction is based ...on the asymmetric (or non-geometric) orbifolds of supersymmetric string vacua. Using the building blocks of their partition functions and their modular properties, we construct theories which would be naturally identified with certain point particle theories including infinite mass spectra, but not with string vacua. They are obviously non-supersymmetric due to the mismatch of the bosonic and fermionic degrees of freedom at each mass level. Nevertheless, it is found that the one-loop cosmological constant vanishes, after removing the parameter effectively playing the role of the UV cut-off. As concrete examples we demonstrate the construction of models based on toroidal asymmetric orbifolds with Lie algebra lattices (Englert–Neveu lattices) by making use of the analysis given in Satoh and Sugawara (2017)
For a finite-type surface
$\mathfrak {S}$
, we study a preferred basis for the commutative algebra
$\mathbb {C}\mathscr {R}_{\mathrm {SL}_3(\mathbb {C})}(\mathfrak {S})$
of regular functions on the
...$\mathrm {SL}_3(\mathbb {C})$
-character variety, introduced by Sikora–Westbury. These basis elements come from the trace functions associated to certain trivalent graphs embedded in the surface
$\mathfrak {S}$
. We show that this basis can be naturally indexed by nonnegative integer coordinates, defined by Knutson–Tao rhombus inequalities and modulo 3 congruence conditions. These coordinates are related, by the geometric theory of Fock and Goncharov, to the tropical points at infinity of the dual version of the character variety.
This substantially enlarged second edition aims to lead a further stage in the computational revolution in commutative algebra. This is the first handbook/tutorial to extensively deal with SINGULAR.
Abstract
We complete the classification of the pointed Hopf algebras with finite Gelfand-Kirillov dimension that are liftings of the Jordan plane over a nilpotent-by-finite group, correcting the ...statement in N. Andruskiewitsch, I. Angiono and I. Heckenberger, Liftings of Jordan and super Jordan planes, Proc. Edinb. Math. Soc., II. Ser. 61(3) (2018), 661–672..
We study S2-orbifolds of N = 1 and N = 2 superconformal vertex algebras. For generic values of the central charge, we determine types of these orbifolds and prove that they are W-algebras. For some ...special rational values of the central charge, we get new examples of rational N = 1 vertex superalgebras. We also investigate S2-orbifold of the Heisenberg–Virasoro vertex algebra.
