20 research outputs found
Classification of involutions on finitary incidence algebras of non-connected posets
Let be the finitary incidence algebra of a non-connected partially
ordered set over a field of characteristic different from . For the
case where every multiplicative automorphism of is inner, we present
necessary and sufficient conditions for two involutions on to be
equivalent
Involutions of the second kind on finitary incidence algebras
Let be a field and a connected partially ordered set. In the first
part of this paper, we show that the finitary incidence algebra of
over has an involution of the second kind if and only if has an
involution and has an automorphism of order . We also give a
characterization of the involutions of the second kind on . In the
second part, we give necessary and sufficient conditions for two involutions of
the second kind on to be equivalent in the case where
and every multiplicative automorphism of is inner
Non-Associative Algebraic Structures: Classification and Structure
These are detailed notes for a lecture on "Non-associative Algebraic
Structures: Classification and Structure" which I presented as a part of my
Agrega\c{c}\~ao em Matem\'atica e Applica\c{c}\~oes (University of Beira
Interior, Covilh\~a, Portugal, 13-14/03/2023)