Results 181 to 190 of about 219,042 (234)
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2001
Abstract In this chapter, we present some very general ideas from the field initiated in its modem form by Garrett Birkhoff and called by him “universal algebra. “ The fundamental notion of universal algebra is that of an algebra. Basically, an algebra is a set together with various operations that take elements of that set and yield ...
J Michael Dunn, Gary M Hardegree
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Abstract In this chapter, we present some very general ideas from the field initiated in its modem form by Garrett Birkhoff and called by him “universal algebra. “ The fundamental notion of universal algebra is that of an algebra. Basically, an algebra is a set together with various operations that take elements of that set and yield ...
J Michael Dunn, Gary M Hardegree
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Journal of Soviet Mathematics, 1991
The survey is based on the material published in the Universal Algebra section of Referativnyĭ Zhurnal Matematika in the period from 1976 till 1988; only the results and the directions are included that were not covered by several similar surveys and are the most promising ones according to the author's opinion.
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The survey is based on the material published in the Universal Algebra section of Referativnyĭ Zhurnal Matematika in the period from 1976 till 1988; only the results and the directions are included that were not covered by several similar surveys and are the most promising ones according to the author's opinion.
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Universal enveloping conformal algebras
Selecta Mathematica, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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International Journal of Algebra and Computation, 2009
We show that a nontrivial example of universal algebra appears in quantum field theory. For a unital C *-algebra [Formula: see text], a sector is a unitary equivalence class of unital *-endomorphisms of [Formula: see text]. We show that the set [Formula: see text] of all sectors of [Formula: see text] is a universal algebra with an N-ary sum which is ...
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We show that a nontrivial example of universal algebra appears in quantum field theory. For a unital C *-algebra [Formula: see text], a sector is a unitary equivalence class of unital *-endomorphisms of [Formula: see text]. We show that the set [Formula: see text] of all sectors of [Formula: see text] is a universal algebra with an N-ary sum which is ...
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Recoupling Lie algebra and universal ω-algebra
Journal of Mathematical Physics, 2004We formulate the algebraic version of recoupling theory suitable for commutation quantization over any gradation. This gives a generalization of graded Lie algebra. Underlying this is the new notion of an ω-algebra defined in this paper. ω-algebra is a generalization of algebra that goes beyond nonassociativity.
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Mathematische Annalen, 2000
Let \(K\) be a field and let \(R\) be a homogeneous \(K\)-algebra, i.e. an algebra of the form \(R=K[x_1,\dots,x_n]/I\) where \(I\) is a homogeneous ideal with respect to deg \(x_i = 1\), the standard grading. A homogeneous algebra \(R\) is said to be universally Koszul if every ideal of \(R\) generated by linear forms has a linear \(R\)-free ...
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Let \(K\) be a field and let \(R\) be a homogeneous \(K\)-algebra, i.e. an algebra of the form \(R=K[x_1,\dots,x_n]/I\) where \(I\) is a homogeneous ideal with respect to deg \(x_i = 1\), the standard grading. A homogeneous algebra \(R\) is said to be universally Koszul if every ideal of \(R\) generated by linear forms has a linear \(R\)-free ...
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Universal Algebra, Algebraic Logic, and Databases
1994Preface. Introduction: 0. General View on Objectives and Contents of the Book. I: Universal Algebra. 1. Sets, Algebras, Models. 2. Fundamental Structures. 3. Categories. 4. The Categories of Sets. Topoi. Fuzzy Sets. 5. Varieties of Algebras. Axiomatizable Classes. 6. Category Algebra and Algebraic Theories. II: Algebraic Logic. 7.
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