Sur Les Train Algèbres De Degré Quatre: Structures Et Classifications

Abstract

We study train algebras of fourth degree, give some genetic examples and explicit the plenary train identities associated. These algebras fall ultimately into four classes; the first two of them do not have 1/2 as train root and thus have idempotents. For these types we provide structure theorems, which are then used for classification purposes in small dimensions.

Key Words:

• Peirce Decomposition
• Plenary train algebras
• Principal train algebras

2000 Mathematics Subject Classification:

• 17D92

ACKNOWLEDGMENTS

Cristián Mallol, Avec l'appui du FONDECYT. N^a 1030294, CONICYT, Chile.

Michelle Nourigat and Richard Varro, Avec l'appui du FONDECYT Coop. Int. N^a 7050242, CONICYT, Chile.

Notes

Communicated by A. Elduque.