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Lectures on graded differential algebras and noncommutative geometry
, 1999
"... These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new developments. ..."
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Cited by 22 (3 self)
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These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new developments.
Gravity on fuzzy spacetime
, 1992
"... Dedicated to Walter Thirring on the occasion of his 70th birthday A review is made of recent efforts to add a gravitational field to noncommutative models of spacetime. Special emphasis is placed on the case which could be considered as the noncommutative analog of a parallelizable spacetime. It i ..."
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Cited by 16 (0 self)
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Dedicated to Walter Thirring on the occasion of his 70th birthday A review is made of recent efforts to add a gravitational field to noncommutative models of spacetime. Special emphasis is placed on the case which could be considered as the noncommutative analog of a parallelizable spacetime. It is argued that, at least in this case, there is a rigid relation between the noncommutative structure of the spacetime on the one hand and the nature of the gravitational field which remains as a ‘shadow ’ in the commutative limit on the other. ESI Preprint 478 (1997). Lecture given at the International Workshop “Mathematical
Some Aspects of Noncommutative Differential Geometry
"... We discuss in some generality aspects of noncommutative differential geometry associated with reality conditions and with differential calculi. We then describe the differential calculus based on derivations as generalization of vector fields, and we show its relations with quantum mechanics. Finall ..."
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Cited by 12 (2 self)
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We discuss in some generality aspects of noncommutative differential geometry associated with reality conditions and with differential calculi. We then describe the differential calculus based on derivations as generalization of vector fields, and we show its relations with quantum mechanics. Finally we formulate a general theory of connections in this framework. 1
Generalized commutation relations and Non linear momenta theories, a close relationship
, 2008
"... A revision of generalized commutation relations is performed, besides a description of Non linear momenta realization included in some DSR theories. It is shown that these propositions are closely related, specially we focus on Magueijo Smolin momenta and Kempf et al. and L.N. Chang generalized comm ..."
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A revision of generalized commutation relations is performed, besides a description of Non linear momenta realization included in some DSR theories. It is shown that these propositions are closely related, specially we focus on Magueijo Smolin momenta and Kempf et al. and L.N. Chang generalized commutators. Due to this, a new algebra arises with its own features that is also analyzed.
Generalized commutation relations and DSR theories, a close relationship
, 2008
"... A revision of generalized commutation relations is performed, beside a description of Deformed Special Relativity (DSR) theories. It is demonstrated that these propositions are very closely related, specially Magueijo Smolin momenta and Kempf et al. and L.N. Chang generalized commutators. Due this, ..."
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A revision of generalized commutation relations is performed, beside a description of Deformed Special Relativity (DSR) theories. It is demonstrated that these propositions are very closely related, specially Magueijo Smolin momenta and Kempf et al. and L.N. Chang generalized commutators. Due this, a new algebra arise with its own features that is also analyzed. 1
On Dynamical Quantization
, 2006
"... Abstract. In this article we review some results obtained from a generalization of quantum mechanics obtained from modification of the canonical commutation relation [q, p] = i¯h. We present some new results concerning relativistic generalizations of previous works, and we calculate the energy spec ..."
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Abstract. In this article we review some results obtained from a generalization of quantum mechanics obtained from modification of the canonical commutation relation [q, p] = i¯h. We present some new results concerning relativistic generalizations of previous works, and we calculate the energy spectrum of some simple quantum systems, using the position and momentum operators of this new formalism.
THE QUEST FOR QUOTIENT RINGS (OF NONCOMMUTATIVE NOETHERIAN RINGS)
"... Articles on the history of mathematics can be written from many different perspectives. Some aim to survey a more or less wide landscape, and require the observer to watch from afar as theories develop and movements are born or become obsolete. At the other extreme, there are those that try to shed ..."
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Articles on the history of mathematics can be written from many different perspectives. Some aim to survey a more or less wide landscape, and require the observer to watch from afar as theories develop and movements are born or become obsolete. At the other extreme, there are those that try to shed light on the history of particular theorems and on the people who created them. This article belongs to this second category. It is an attempt to explain Goldie’s theorems on quotient rings in the context of the life and times of the man who discovered them. 1. Fractions Fractions are at least as old as civilisation. The Egyptian scribes of 3,000 years ago were very skilful in their manipulation as attested by many ancient papyri. To the Egyptians and Mesopotamians, fractions were just tools to find the correct answer to practical problems in land surveying and accounting. However, the situation changed dramatically in Ancient Greece. To the Greek philosophers, number meant positive integer, and 1 was ‘the unity’, and as such, had to be indivisible. So how could ‘half ’ be a number, since ‘half the unity ’ did not
Lectures On Graded Differential Algebras And Noncommutative Geometry
, 2000
"... These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new developments. LPTORSAY 99/100 Keywords : graded differential alge ..."
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These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new developments. LPTORSAY 99/100 Keywords : graded differential algebras; categories of algebras; bimodules; noncommutative differential calculus; noncommutative symplectic geometry. MSC classification: 16D20, 18B99, 51P05, 53A99, 81Q99. To be published in the Proceedings of the Workshop on Noncommutative Differential Geometry and its Application to Physics, ShonanKokusaimura, Japan, May 31  June 4, 1999. 1 Unit'e Mixte de Recherche du Centre National de la Recherche Scientifique  UMR 8627 1 Contents 1 Introduction 3 2 Graded differential algebras 10 3 Examples related to Lie algebras 15 4 Examples related to associative algebras 20 5 Categories of algebras 26 6 First order differential calculi 31 7 Higher order differential calculi 36 8 Diagonal an...