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

• 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

• [1] G. Grätzer, General Lattice Theory, Academic Press, New York, 1978.
• [2] Kelly and I. Rival, Planar lattices, Canad. J. Math. 27 (1975), 636-665.
• [3] P. Leroux and J. Saraille, Structure of incidence algebras of graphs, Comm. in Algebra 9 (1981), 1479-1517.
• [4] J. Neggers, Partially ordered sets and groupoids, Kyungpook Math. J. 16 (1976), 7-20.
• [5] J. Neggers and H. S. Kim, Modular semigroups and posets, Semigroup Forum 53 (1996), 57-62.
• [6] J. Neggers and H. S. Kim, Self-distributive modular pogroupoids and posets, Kyungpook Math. J. 38 (1998), 407-409.
• [7] J. Neggers and H. S. Kim, Basic Posets, World Scientific Publishing Co., New Jersey, 1998.
• [8] J. Neggers, Y. H. Kim and H. S. Kim, Incomparability and Transitivity (submitted).
• [9] J. Neggers, Y. H. Kim and H. S. Kim, Varieties of posets and poset geometry, Math. Slovaca (to appear).
• [10] E. Spiegel, Radicals of Incidence Algebras, Comm. in Algebra 22 (1994), 139-149.