Results 151 to 160 of about 137,153 (176)
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Non-commutative differential calculus and q-analysis
Journal of Physics A: Mathematical and General, 1992Summary: Starting from the formulation of covariant non-commutative differential calculus recently given by Wess and Zumino we construct a deformation of the Virasoro algebra, which allow us to identify the variables and differential operators on the quantum plane \(\mathbb{R}^ 2_ q\) to those on the classical plane \(\mathbb{R}^ 2\).
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Differential Calculus as Part of Commutative Algebra
2020This is the central chapter of the book. At the beginning of the chapter, it is shown that the classical definitions of the calculus or of differential geometry, say that of the derivative or tangent vector, are unsatisfactory, being of descriptive nature, and conceptually correct definitions are needed.
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On Nilpotent Products of Cyclic Groups—Reexamined by the Commutator Calculus
Canadian Journal of Mathematics, 1975Ruth R. Struik investigated the nilpotent group , where G is a free product of a finite number of cyclic groups, not all of which are of infinite order, and Gm is the mth subgroup of the lower central series of G. Making use of the “collection process” first given by Philip Hall in [8], she determined completely for 1 ≦ n ≦ p + 1, where p is the ...
Waldinger, Hermann V. +1 more
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Linear axiomatics of commutative product-free Lambek calculus
Studia Logica, 1990Axiomatics which do not employ rules of inference other than the cut rule are given for commutative product-free Lambek calculus in two variants: with and without the empty string. Unlike the former variant, the latter one turns out not to be finitely axiomatizable in that way.
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Calculus over Commutative Algebras: A Concise User Guide
Acta Applicandae Mathematica, 1997In this paper, I. S. Krasil'shchik presents the basic facts and definitions concerning linear differential operators and jets for modules over a commutative associative unitary \(\kappa\)-algebra. The paper is a well written exposition of the subject with presentation of the Spencer Diff-complex, the de Rham complex and the Spencer jet-complex.
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A functional calculus in a non commutative setting
2007In this paper we announce the development of a functional calculus for operators defined on quaternionic Banach spaces. The definition is based on a new notion of slice regularity and the key tools are a new resolvent operator and a new eigenvalue problem. This approach allows us to deal both with bounded and unbounded operators.
COLOMBO, FABRIZIO +3 more
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Commutator Calculus and Groups of Homotopy Classes
1981A fundamental problem of algebraic topology is the classification of homotopy types and homotopy classes of maps. In this work the author extends results of rational homotopy theory to a subring of the rationale. The methods of proof employ classical commutator calculus of nilpotent group and Lie algebra theory and rely on an extensive and systematic ...
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A Functional Calculus for Pairs of Commuting Contractions
Journal of the London Mathematical Society, 1974Briem, E. +2 more
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