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10,257
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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regular fashion. These arise regularly in connection with extremal structures: such structures often have an unexpected degree of regularity and, because of this, often give rise to an association scheme. This in turn leads to a semisimple commutative algebra and the representation theory of this algebra
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
Using Linear Algebra for Intelligent Information Retrieval
 SIAM REVIEW
, 1995
"... Currently, most approaches to retrieving textual materials from scientific databases depend on a lexical match between words in users' requests and those in or assigned to documents in a database. Because of the tremendous diversity in the words people use to describe the same document, lexical ..."
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Cited by 676 (18 self)
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, lexical methods are necessarily incomplete and imprecise. Using the singular value decomposition (SVD), one can take advantage of the implicit higherorder structure in the association of terms with documents by determining the SVD of large sparse term by document matrices. Terms and documents represented
EXTENSIONS OF ASSOCIATIVE ALGEBRAS
, 908
"... Abstract. In this paper, we give a purely cohomological interpretation of the extension problem for associative algebras; that is the problem of extending an associative algebra by another associative algebra. We then give a similar interpretation of infinitesimal deformations of extensions. In part ..."
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Cited by 3 (3 self)
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Abstract. In this paper, we give a purely cohomological interpretation of the extension problem for associative algebras; that is the problem of extending an associative algebra by another associative algebra. We then give a similar interpretation of infinitesimal deformations of extensions
Integrable Evolution Equations on Associative Algebras
, 1997
"... This paper surveys the classi cation of integrable evolution equations whose eld variables take values in an associative algebra, which includes matrix, Clifford, and group algebra valued systems. A variety of new examples of integrable systems possessing higher order symmetries are presented. Symm ..."
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Cited by 70 (10 self)
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This paper surveys the classi cation of integrable evolution equations whose eld variables take values in an associative algebra, which includes matrix, Clifford, and group algebra valued systems. A variety of new examples of integrable systems possessing higher order symmetries are presented
Basic cohomology of associative algebras
 Journal of Pure and Applied Algebra
, 1996
"... We define a new cohomology for associative algebras which we compute for algebras with units. L.P.T.H.E.ORSAY 94/10 1 ..."
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Cited by 2 (2 self)
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We define a new cohomology for associative algebras which we compute for algebras with units. L.P.T.H.E.ORSAY 94/10 1
On the operad of associative algebras with derivation
"... We study the operad of associative algebras equipped with a derivation. We show that it is determined by polynomials in several variables and substitution. Replacing polynomials by rational functions gives an operad which is isomorphic to the operad of “moulds”. It provides an efficient environmen ..."
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Cited by 7 (1 self)
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We study the operad of associative algebras equipped with a derivation. We show that it is determined by polynomials in several variables and substitution. Replacing polynomials by rational functions gives an operad which is isomorphic to the operad of “moulds”. It provides an efficient
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