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OPERADS AND PROPS
, 2006
"... We review definitions and basic properties of operads, PROPs and algebras over these structures. ..."
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Cited by 8 (0 self)
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We review definitions and basic properties of operads, PROPs and algebras over these structures.
NATURAL DIFFERENTIAL OPERATORS AND GRAPH COMPLEXES
, 2007
"... We show how the machine invented by S. Merkulov [19, 20, 22] can be used to study and classify natural operators in differential geometry. We also give an interpretation of graph complexes arising in this context in terms of representation theory. As application, we prove several results on classifi ..."
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Cited by 4 (3 self)
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We show how the machine invented by S. Merkulov [19, 20, 22] can be used to study and classify natural operators in differential geometry. We also give an interpretation of graph complexes arising in this context in terms of representation theory. As application, we prove several results on classification of natural operators acting on vector fields and connections.
Symmetric Boolean algebras
"... We define Boolean algebras in the linear context and study its symmetric powers. We give explicit formulae for products in symmetric Boolean algebras of various dimensions. We formulate symmetric forms of the inclusionexclusion principle. ..."
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Cited by 3 (3 self)
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We define Boolean algebras in the linear context and study its symmetric powers. We give explicit formulae for products in symmetric Boolean algebras of various dimensions. We formulate symmetric forms of the inclusionexclusion principle.
PROPped up graph cohomology
, 2007
"... We consider graph complexes with a flow and compute their cohomology. More specifically, we prove that for a PROP generated by a Koszul dioperad, the corresponding graph complex gives a minimal model of the PROP. We also give another proof of the existence of a minimal model of the bialgebra PROP ..."
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We consider graph complexes with a flow and compute their cohomology. More specifically, we prove that for a PROP generated by a Koszul dioperad, the corresponding graph complex gives a minimal model of the PROP. We also give another proof of the existence of a minimal model of the bialgebra PROP from [14]. These results are based on the useful notion of a 1 PROP introduced by Kontsevich 2 in [9].