Arkady Tsurkov
USP, Brazil
Strongly stable automorphisms of the categories of the finitely generated free linear algebras of the classical varieties.
May 16, 2012
Abstract: We consider the classical varieties of linear algebras:

• Variety of all linear algebras,
• Variety of all power associative algebras,
• Variety of all alternative algebras,
• Variety of all commutative algebras,
• Variety of all Jordan algebras,
• Arbitrary subvarieties of the variety of all anticommutative algebras,
• Variety of all nilpotent algebras with degree of nilpotence no more than 3,
• Variety of all nilpotent algebras with degree of nilpotence no more than 4.

We consider in all this varieties the category of the finitely generated free algebras of this variety and calculate the group S of all strongly stable automorphisms of this category. After that we calculate the quotient group A/Y, where A is the group of all automorphisms of this category and Y is the group of all inner automorphisms of this category. This problem is important for the universal algebraic geometry of linear algebras.