No Access

Classification of involutions on finitary incidence algebras

Rosali Brusamarello

Departamento de Matemática, Universidade Estadual de Maringá, Avenida Colombo, 5790, Maringá, PR, 87020-900, Brazil

Search for more papers by this author

Érica Zancanella Fornaroli

Departamento de Matemática, Universidade Estadual de Maringá, Avenida Colombo, 5790, Maringá, PR, 87020-900, Brazil

Search for more papers by this author

, and

Ednei Aparecido Santulo, Júnior

Departamento de Matemática, Universidade Estadual de Maringá, Avenida Colombo, 5790, Maringá, PR, 87020-900, Brazil

Search for more papers by this author

https://doi.org/10.1142/S0218196714500477Cited by:11 (Source: Crossref)

Abstract

Let X be a connected partially ordered set and let K be a field of characteristic different from 2. We present necessary and sufficient conditions for two involutions on the finitary incidence algebra of X over K, FI(X), to be equivalent in the case when every multiplicative automorphism of FI(X) is inner. To get the classification of involutions we extend the concept of multiplicative automorphism to finitary incidence algebras and prove the Decomposition Theorem of involutions of [Anti-automorphisms and involutions on (finitary) incidence algebras, Linear Multilinear Algebra60 (2012) 181–188] for finitary incidence algebras.

Keywords:

AMSC: 16W10, 16W20, 05B20

References

K. Baclawski , Proc. Amer. Math. Soc. 36 , 351 ( 1972 ) . Crossref, Web of Science, Google Scholar
R. Brusamarello , E. Z. Fornaroli and E. A. Santulo Jr. , Comm. Algebra 39 , 1941 ( 2011 ) . Crossref, Web of Science, Google Scholar
R. Brusamarello , E. Z. Fornaroli and E. A. Santulo Jr. , Linear Multilinear Algebra 60 , 181 ( 2012 ) . Crossref, Web of Science, Google Scholar
R. Brusamarello , E. Z. Fornaroli and E. A. Santulo Jr. , Comm. Algebra 43 , 726 ( 2015 ) . Crossref, Web of Science, Google Scholar
N. S. Khripchenko, Algebra Discrete Math. 9(2), 78 (2010). Google Scholar
N. S. Khripchenko and B. V. Novikov, Comm. Algebra 37(5), 1670 (2009). Crossref, Web of Science, Google Scholar
E. Spiegel and C. O'Donnell , Incidence Algebras , Monographs and Textbooks in Pure and Applied Mathematics 206 ( Marcel Dekker Inc. , New York , 1997 ) . Google Scholar
R. P. Stanley , Bull. Amer. Math. Soc. 76 , 1236 ( 1970 ) . Crossref, Web of Science, Google Scholar