Operator algebras, varieties of algebras and related topics
admit pure local derivations
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April 15-16
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admit pure local derivations, that is, local derivations which are not derivation. Further we
consider 2-local derivations on the octonion algebra O(F) over an algebraically closed field F and prove that every 2-local derivation on O(F) is a derivation. But for the field R of real numbers 2-local derivations on the octonian algebra O(R) form a Lie algebra which is essentially larger than the Lie algebra g 2 (R) of derivations. we apply these results to problems for the simple 7-dimensional Malcev algebra. Further we shall give a general form of local automorphisms on the octonion algebra O(F). This description implies that the group of all local automorphisms on O(F) is isomorphic to the group O 7 (F) of all orthogonal 7 × 7-matrices over F, and it is essentially larger than the group of all automorphisms. We also consider 2-local automorphisms on the octonion algebra O(F) over an algebraically closed field F and prove that every 2-local automorphism on O(F) is an automorphism. At the same time the group of 2-local automorphisms of O(R) is larger than the group of automorphisms of O(R). As a corollary we obtain descriptions of local and 2-local automorphisms of seven dimensional simple Malcev algebra. Speaker: V. Dotsenko (University of Strasbourg) Title: Varieties of algebras: an introduction Abstract: This is a survey talk on some aspects of the theory of algebras with polynomial identities. I shall recall the relevant definitions and highlight some classical results of this theory from 1950s to the present time. Speaker: X. Garcia-Martinez (Universidade de Vigo) Download 435.53 Kb. Do'stlaringiz bilan baham: |
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