Results 131 to 140 of about 11,813 (170)

Generalized Commutator Formulas

Communications in Algebra, 2011
Let A be an algebra which is a direct limit of module finite algebras over a commutative ring R with 1. Let I, J be two-sided ideals of A, GL n (A, I) the principal congruence subgroup of level I in GL n (A), and E n (A, I) the relative elementary subgroup of level I.
Hazrat, Roozbeh (R16959), Zhang, Zuhong
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NON-COMMUTATIVE POLYNOMIAL RECIPROCITY FORMULAE

International Journal of Mathematics, 2001
We prove non-commutative reciprocity formulae for certain polynomials using Fox's free differential calculus. The abelianizations of these reciprocity formulae rediscover the polynomial reciprocity formulae of Carlitz and Berndt–Dieter. Further, many other reciprocity formulae related to Dedekind sums are rederived from our polynomial reciprocity ...
Fukuhara, Shinji, Matsumoto, Yukio, Yui, Noriko   +2 more
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Commutation formulae in conformal finsler space — I

Annali di Matematica Pura ed Applicata, 1971
The commutation formulae in Finsler space have been studied by several authors. In this paper we have obtained various forms of commutation formulae for different geometric entities of the conformal Finsler space.
Lal, K. B., Singh, S. S.
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Unrelativized Standard Commutator Formula

Journal of Mathematical Sciences, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A non-commutative binomial formula

Journal of Geometry and Physics, 2000
The classical binomial formula \[ (x+y)^n=\sum_{k=0}^n\binom{n}{k}y^kx^{n-k},\quad n=0,1,2,\ldots \] holds in an arbitrary ring with unity provided that \(xy=yx\). In [\textit{M. P. Schützenberger}, C.R. Acad. Sci., Paris 236, 352-353 (1953; Zbl 0051.09401)] it is shown that \[ (x+y)^n=\sum_{k=0}^n\frac{(q;q)_n}{(q;q)_k(q;q)_{n-k}}y^kx^{n-k}, \quad n=0,
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A non‐commutative Landau‐Zener formula

Mathematische Nachrichten, 2004
AbstractWe study semi‐classical measures of families of solutions to a 2 × 2 Dirac system with 0 mass, which presents bands crossing. We focus on constant electro‐magnetic fields. The fact that these fields are orthogonal or not leads to different geometric situations. In the first case, one reduces to some well‐understood model problem.
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Galois Groups, Abstract Commutators, and Hopf Formula

Applied Categorical Structures, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Geometric Formula for Current-Algebra Commutation Relations

Physical Review, 1969
Summary: A purely algebraic formalism is introduced in order to describe the relation between current algebras and Lagrangian field theory. It is then applied to the description in differential-geometric terms of the equal-time commutation relations for currents defined by Lagrangians derived from Riemannian metrics on internal-symmetry spaces.
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The commutation formulae in a finsler space. I

Annali di Matematica Pura ed Applicata, 1967
In a previous paper [2] some commutation formulae have been established on the principle of mathematical induction. The present paper includes the commutation formulae involving the covariant derivatives of Cartan and of Berwald. In this paper, too, the method of mathematical induction has been used.
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A useful formula for evaluating commutators

Journal of Mathematical Physics, 1983
We present the derivation of a useful formula for evaluating commutators of the form [A, f (B)] and [ f (A),B], where the nested commutators [A,[A,[⋅⋅⋅[A[A,B]]⋅⋅⋅]]] and [[[⋅⋅⋅[[A,B],B]⋅⋅⋅],B],B] do not vanish in general. The use of this formula is illustrated by a simple example.
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