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Representation Theory of Artin Algebras
 Studies in Advanced Mathematics
, 1994
"... The representation theory of artin algebras, as we understand it today, is a relatively new area of mathematics, as most of the main developments have occurred ..."
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Cited by 645 (10 self)
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The representation theory of artin algebras, as we understand it today, is a relatively new area of mathematics, as most of the main developments have occurred
Algebraic Graph Theory
, 2011
"... Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area is the investiga ..."
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Cited by 892 (13 self)
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Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area
Ktheory for operator algebras
 Mathematical Sciences Research Institute Publications
, 1998
"... p. XII line5: since p. 12: I blew this simple formula: should be α = −〈ξ, η〉/〈η, η〉. p. 2 I.1.1.4: The RieszFischer Theorem is often stated this way today, but neither Riesz nor Fischer (who worked independently) phrased it in terms of completeness of the orthogonal system {e int}. If [a, b] is a ..."
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Cited by 558 (0 self)
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p. XII line5: since p. 12: I blew this simple formula: should be α = −〈ξ, η〉/〈η, η〉. p. 2 I.1.1.4: The RieszFischer Theorem is often stated this way today, but neither Riesz nor Fischer (who worked independently) phrased it in terms of completeness of the orthogonal system {e int}. If [a, b] is a bounded interval in R, in modern language the original statement of the theorem was that L 2 ([a, b]) is complete and abstractly isomorphic to l 2. According to [Jah03, p. 385], the name “Hilbert space ” was first used in 1908 by A. Schönflies, apparently to refer to what we today call l 2. Von Neumann used the same name for Hilbert spaces in the modern sense (complete inner product spaces), which he defined in 1928. p. 3 line6: At the end of the line, 2ɛ should be 4ɛ. p. 3 I.1.2.3: The statement that a dense subspace of a Hilbert space H contains an orthonormal basis for H can be false if H is nonseparable. In fact, I. Farah (private communication) has shown that a Hilbert space of dimension 2ℵ0 has a dense subspace which does not contain any uncountable orthonormal set. A similar example was obtained by Dixmier [Dix53]. p. 89 I.2.4.3(i): Some of the statements on p. 9 can be false if the measure space is not σfinite. p. 13: add after I.2.6.16: I.2.6.17. If X is a compact subset of C not containing 0, and k ∈ N, there is in general no bound on the norm of T −1 as T ranges over all operators with ‖T ‖ ≤ k and σ(T) ⊆ X. For example, let Sn ∈ L(l 2) be the truncated shift: Sn(α1, α2,...) = (0, α1, α2,..., αn, 0, 0,...) and let Tn = I − Sn. ‖Sn ‖ = 1, so ‖Tn ‖ ≤ 2 for all n. Since Sn is nilpotent, σ(Sn) = {0}, so σ(Tn) = {1} for all n. Tn is invertible, with T −1 n = I + Sn + ξ1 ‖ = √ n + 1, so ‖T −1
Algebraic theories
, 2004
"... In memory of Grigore C. Moisil who supervised my first steps in research. Abstract. We presents the algebraic theories over an arbitrary monoid, main properties and calculus rules. Ordered, rationaly closed and ωcontinuous theories on one hand and matrix and complete matrix theories on the other ha ..."
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In memory of Grigore C. Moisil who supervised my first steps in research. Abstract. We presents the algebraic theories over an arbitrary monoid, main properties and calculus rules. Ordered, rationaly closed and ωcontinuous theories on one hand and matrix and complete matrix theories on the other
Homological Algebra of Mirror Symmetry
 in Proceedings of the International Congress of Mathematicians
, 1994
"... Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual Ca ..."
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Cited by 523 (3 self)
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Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual
ALGEBRAIC THEORY OF AFFINE CURVATURE TENSORS
"... Algebraic theory of affine curvature tensors by ..."
An Algebraic Theory of
"... We give an algebraic formalization of SLDtrees and their abstractions (ob servables). We can state and prove in the framework several useful theorems (ANDcompositionality, correctness and full abstraction of the denotation, equivalent topdown and bottomup constructions) about semantic properties ..."
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Cited by 1 (0 self)
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We give an algebraic formalization of SLDtrees and their abstractions (ob servables). We can state and prove in the framework several useful theorems (ANDcompositionality, correctness and full abstraction of the denotation, equivalent topdown and bottomup constructions) about semantic
Process algebra for synchronous communication
 Inform. and Control
, 1984
"... Within the context of an algebraic theory of processes, an equational specification of process cooperation is provided. Four cases are considered: free merge or interleaving, merging with communication, merging with mutual exclusion of tight regions, and synchronous process cooperation. The rewrite ..."
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Cited by 426 (68 self)
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Within the context of an algebraic theory of processes, an equational specification of process cooperation is provided. Four cases are considered: free merge or interleaving, merging with communication, merging with mutual exclusion of tight regions, and synchronous process cooperation. The rewrite
The algebraic theory of torsion I. Foundations
 in Proc. I983 Rutgers Topology Conference, Springer Lecture Notes in Math. 1126
, 1985
"... The algebraic theory of torsion developed here takes values ..."
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Cited by 3 (1 self)
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The algebraic theory of torsion developed here takes values
Are operads algebraic theories? The
 Bulletin of the London Mathematical Society
"... www.maths.gla.ac.uk/∼tl I exhibit a pair of nonsymmetric operads that, although not themselves isomorphic, induce isomorphic monads. The existence of such a pair implies that if ‘algebraic theory ’ is understood as meaning ‘monad’, operads cannot be regarded as algebraic theories of a special kind. ..."
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www.maths.gla.ac.uk/∼tl I exhibit a pair of nonsymmetric operads that, although not themselves isomorphic, induce isomorphic monads. The existence of such a pair implies that if ‘algebraic theory ’ is understood as meaning ‘monad’, operads cannot be regarded as algebraic theories of a special kind.
Results 1  10
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