Search results for "Commutative property"
showing 10 items of 34 documents
Some aspects of deformations of supersymmetric field theories
2000
We investigate some aspects of Moyal-Weyl deformations of superspace and their compatibility with supersymmetry. For the simplest case, when only bosonic coordinates are deformed, we consider a four dimensional supersymmetric field theory which is the deformation of the Wess-Zumino renormalizable theory of a chiral superfield. We then consider the deformation of a free theory of an abelian vector multiplet, which is a non commutative version of the rank one Yang-Mills theory. We finally give the supersymmetric version of the $\alpha'\mapsto 0$ limit of the Born-Infeld action with a B-field turned on, which is believed to be related to the non commutative U(1) gauge theory.
Non-commutative geometry and supersymmetry II
1991
Abstract Extending results of a previous work [Phys. Lett. B 260 (1991) 359], we establis that anothe non-commutative model proposed by Balakrishna, Gursey and Wali may be expressed as a Yang-Mills theory of a graded Lie group.
Perturbative BF-Yang–Mills theory on noncommutative
2000
A U(1) BF-Yang-Mills theory on noncommutative ${\mathbb{R}}^4$ is presented and in this formulation the U(1) Yang-Mills theory on noncommutative ${\mathbb{R}}^4$ is seen as a deformation of the pure BF theory. Quantization using BRST symmetry formalism is discussed and Feynman rules are given. Computations at one-loop order have been performed and their renormalization studied. It is shown that the U(1) BFYM on noncommutative ${\mathbb{R}}^4$ is asymptotically free and its UV-behaviour in the computation of the $\beta$-function is like the usual SU(N) commutative BFYM and Yang Mills theories.
A pointwise selection principle for metric semigroup valued functions
2008
Abstract Let ∅ ≠ T ⊂ R , ( X , d , + ) be an additive commutative semigroup with metric d satisfying d ( x + z , y + z ) = d ( x , y ) for all x , y , z ∈ X , and X T the set of all functions from T into X . If n ∈ N and f , g ∈ X T , we set ν ( n , f , g , T ) = sup ∑ i = 1 n d ( f ( t i ) + g ( s i ) , g ( t i ) + f ( s i ) ) , where the supremum is taken over all numbers s 1 , … , s n , t 1 , … , t n from T such that s 1 ⩽ t 1 ⩽ s 2 ⩽ t 2 ⩽ ⋯ ⩽ s n ⩽ t n . We prove the following pointwise selection theorem: If a sequence of functions { f j } j ∈ N ⊂ X T is such that the closure in X of the set { f j ( t ) } j ∈ N is compact for each t ∈ T , and lim n → ∞ ( 1 n lim N → ∞ sup j , k ⩾ N , j…
Matrix algebras with degenerate traces and trace identities
2022
In this paper we study matrix algebras with a degenerate trace in the framework of the theory of polynomial identities. The first part is devoted to the study of the algebra $D_n$ of $n \times n$ diagonal matrices. We prove that, in case of a degenerate trace, all its trace identities follow by the commutativity law and by pure trace identities. Moreover we relate the trace identities of $D_{n+1}$ endowed with a degenerate trace, to those of $D_n$ with the corresponding trace. This allows us to determine the generators of the trace T-ideal of $D_3$. In the second part we study commutative subalgebras of $M_k(F)$, denoted by $C_k$ of the type $F + J$ that can be endowed with the so-called st…
Trace identities and almost polynomial growth
2021
In this paper we study algebras with trace and their trace polynomial identities over a field of characteristic 0. We consider two commutative matrix algebras: $D_2$, the algebra of $2\times 2$ diagonal matrices and $C_2$, the algebra of $2 \times 2$ matrices generated by $e_{11}+e_{22}$ and $e_{12}$. We describe all possible traces on these algebras and we study the corresponding trace codimensions. Moreover we characterize the varieties with trace of polynomial growth generated by a finite dimensional algebra. As a consequence, we see that the growth of a variety with trace is either polynomial or exponential.
Extensions of the Noncommutative Integration
2016
In this paper we will continue the analysis undertaken in Bagarello et al. (Rend Circ Mat Palermo (2) 55:21–28, 2006), Bongiorno et al. (Rocky Mt J Math 40(6):1745–1777, 2010), Triolo (Rend Circ Mat Palermo (2) 60(3):409–416, 2011) on the general problem of extending the noncommutative integration in a *-algebra of measurable operators. As in Aiena et al. (Filomat 28(2):263–273, 2014), Bagarello (Stud Math 172(3):289–305, 2006) and Bagarello et al. (Rend Circ Mat Palermo (2) 55:21–28, 2006), the main problem is to represent different types of partial *-algebras into a *-algebra of measurable operators in Segal’s sense, provided that these partial *-algebras posses a sufficient family of pos…
Extended pseudo-fermions from non commutative bosons
2013
We consider some modifications of the two dimensional canonical commutation relations, leading to {\em non commutative bosons} and we show how biorthogonal bases of the Hilbert space of the system can be obtained out of them. Our construction extends those recently introduced by one of us (FB), modifying the canonical anticommutation relations. We also briefly discuss how bicoherent states, producing a resolution of the identity, can be defined.
Identities of sums of commutative subalgebras
1994
SiaR un'algebra associativa tale cheR=A+B conA, B sottoalgebre commutative. Si dimostra cheR soddisfa l'identita polinomiale [[x,y],[z,t]]≡0 e che, seV e la varieta determinata da questa identita,V e la piu piccola varieta contenente tutte le algebre somma di sottoalgebre commutative. Si determina inoltre la struttura delle algebre libere diV.
Commutativity conditions on rings
1991
We prove the following result: let R be an arbitrary ring with centre Z such that for every x, y ∈ R, there exists a positive integer n = n(x, y) ≥ 1 such that (xy)n − ynxn ∈ Z and (yx)n − xnyn ∈ Z; then, if R has no non-zero nil ideals, R is commutative. We also prove a result on commutativity of general rings: if R is r!-torsion free and for all x, y ∈ R, [xr, ys] = 0 for fixed integers r ≥ s ≥ 1, then R is commutative. As a corollary we obtain that if R is (n + 1)!-torsion free and there exists a fixed n ≥ 1 such that (xy)n − ynxn = (yx)n − xnyn ∈ Z for all x, y ∈ R, then R is commutative.