Algebras associated with posets

• Autorzy: Neggers J. , Kim H. S.
• Języki publikacji: EN

Abstrakty

EN

In this paper we introduce a class of algebras whose bases over a field K are pogroupoids. We discuss several properties of these algebras as they relate to the structure of their associated pogroupoids and through these to the associated posets also. In particular the Jacobi form is O precisely when the pogroupoid is a semigroup, precisely when the posets is (C2 + 1)-free. Thus, it also follows that a pg-algebra KS over a field K is a Lie algebra with respect to the commutator product iff its associated posets S(<) is (C2 +1)-free. The ideals generated by commutators have some easily identifiable properties m terms of the incomparability graph of the posets associated with the pogroupoid base of the algebra. We conjecture that a fundamental theorem on the relationship between isomorphic algebras and isomorphic pogroupoids holds as well.

Słowa kluczowe

EN

posets; pogroupoid; Harris diagram; Jacobi identity; Lie algebra

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2001
• Tom: Vol. 34, nr 1
• Strony: 13--23
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Neggers J.

• Department of Mathematics University of Alabama Tuscaloosa, AL 35487-0350, USA

autor

Kim H. S.

• Department of Mathematics Hanyang University Seoul 133-791, Korea

Bibliografia

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