2,956 research outputs found
Integrals, quantum Galois extensions and the affineness criterion for quantum Yetter-Drinfel'd modules
We introduce and study a general concept of integral of a threetuple (H, A,
C), where H is a Hopf algebra acting on a coalgebra C and coacting on an
algebra A. In particular, quantum integrals associated to Yetter-Drinfel'd
modules are defined. Let A be an H-bicomodule algebra, be the
category of (generalized) Yetter-Drinfel'd modules and the subalgebra of
coinvariants of the Verma structure of . We introduce the concept of quantum
Galois extensions and we prove the affineness criterion in a quantum version.Comment: latex 32 pg. J. Algebra, to appea
Towards a generalisation of formal concept analysis for data mining purposes
In this paper we justify the need for a generalisation of Formal
Concept Analysis for the purpose of data mining and begin the
synthesis of such theory. For that purpose, we first review semirings and
semimodules over semirings as the appropriate objects to use in abstracting
the Boolean algebra and the notion of extents and intents, respectively.
We later bring to bear powerful theorems developed in the field
of linear algebra over idempotent semimodules to try to build a Fundamental
Theorem for K-Formal Concept Analysis, where K is a type of
idempotent semiring. Finally, we try to put Formal Concept Analysis in
new perspective by considering it as a concrete instance of the theory
developed
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