Let $R$ be a prime ring with extended centroid $C$, $H$ a generalized derivation of $R$ and $ngeq 1$ a fixed integer. In this paper we study the situations: (1) If $(H(xy))^n =(H(x))^n(H(y))^n$ for all $x,yin R$; (2) obtain some related result in case $R$ is a noncommutative Banach algebra and $H$ is continuous or spectrally bounded.

The article concerns the subalgebra U v (w) of the quantized universal enveloping algebra of the complex Lie algebra sln+1 associated with a particular Weyl group element of length 2n. We verify that U v (w) can be endowed with the structure of a quantum cluster algebra of type An. The quantum cluster algebra is a deformation of the ordinary cluster algebra Geiß-Leclerc-Schröer attached to w us...

We propose a new method to quantize gauge theories formulated on a canonical noncommutative spacetime with fields and gauge transformations taken in the enveloping algebra. We show that the theory is renormalizable at one loop and compute the beta function and show that the spin dependent contribution to the anomalous magnetic moment of the fermion at one loop has the same value as in the commu...

Canonical extensions were first studied, in the context of Boolean algebras with operators (BAOs), in the classic work of B. Jónsson and A. Tarski [12]. The development of a corresponding theory in a less restricted setting than that of BAOs lagged far behind. However major advances have been made in the past ten years by M. Gehrke in collaboration with B. Jónsson, J. Harding, Y. Venema and oth...

Let H be a non semi-simple Ariki-Koike algebra. According to [19] and [15], there is a generalisation of Lusztig’s a-function which induces a natural combinatorial order (parametrised by a tuple m) on Specht modules. In some cases, Geck and Jacon have proved that this order makes unitriangular the decomposition matrix of H . The algebra H is then said to admit a "canonical basic set". We fully ...

The mathematical formalism for linear quantum field theory on curved spacetime depends in an essential way on the assumption of global hyperbolicity. Physically, what lie at the foundation of any formalism for quantization in curved spacetime are the canonical commutation relations, imposed on the field operators evaluated at a global Cauchy surface. In the algebraic formulation of linear quant...

Let G be a connected semisimple algebraic group over an algebraically closed field of characteristic zero. A canonical presentation by generators and relations of the algebra of regular functions on G is found. The conjectures of D.Flath and J.Towber, [FT], are proved. (1) Let G be a connected semisimple algebraic group over an algebraically closed field k of characteristic zero. We obtain here...

Dense linear algebra codes are often expressed and coded in terms of BLAS calls. This approach, however, achieves suboptimal performance due to the overheads associated to such calls. Taking as an example the dense Cholesky factorization of a symmetric positive definite matrix we show that the potential of non-canonical data structures for dense linear algebra can be better exploited with the u...

A variety V of Boolean algebras with operators is singleton-persistent if it contains a complex algebra whenever it contains the subalgebra generated by the singletons. V is atom-canonical if it contains the complex algebra of the atom structure of any of the atomic members of V . This paper explores relationships between these “persistence” properties and questions of whether V is generated by...

We first observe that the relations of the canonical generating isometries of the Cuntz algebra ON are naturally related to the N-colored Catalan numbers. For a directed graph G, we generalize the Catalan numbers by using the canonical generating partial isometries of the Cuntz-Krieger algebra O AG for the transition matrix A of G. The generalized Catalan numbers cGn , n = 0, 1, 2, . . . enumer...