Universal decomposition algebras and the classification of 2-generated non-primitive axial algebras of Jordan type

2022/07/04 by Yabe, Takahiro
#17A60 #17A99 #17C27 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2207.01225

Abstract

Decomposition algebras and axial decomposition algebras are classes of commutative nonassociative algebras which are generalizations of axial algebras. The classes decomposition algebras, axial decomposition al;gebras and non-primitive axial algebras also have univesal algebras. Furthermore, by using the existence of a universal algebra, 2-generated non-primitive axial algebras of Jordan type is classified.

Related

• Axes of Jordan type in non-commutative algebras
• Axial algebras of Jordan and Monster type
• Primitive axial algebras are of Jordan type
• Central extensions of axial algebras
• Quasi-definite axial algebras of Jordan type half