Algebras, Dialgebras, and Polynomial Identities

R. Bremner, Murray. "Algebras, Dialgebras, and Polynomial Identities." Serdica Mathematical Journal 38.1-3 (2012): 91-136. <http://eudml.org/doc/288276>.

@article{R2012,
abstract = {2010 Mathematics Subject Classification: Primary 17A30. Secondary 16R10, 17-08, 17A32,This is a survey of some recent developments in the theory of associative and nonassociative dialgebras, with an emphasis on polynomial identities and multilinear operations. We discuss associative, Lie, Jordan, and alternative algebras, and the corresponding dialgebras; the KP algorithm for converting identities for algebras into identities for dialgebras; the BSO algorithm for converting operations in algebras into operations in dialgebras; Lie and Jordan triple systems, and the corresponding disystems; and a noncommutative version of Lie triple systems based on the trilinear operation abc − bca. The paper concludes with a conjecture relating the KP and BSO algorithms, and some suggestions for further research. Most of the original results are joint work with Raúl Felipe, Luiz A. Peresi, and Juana Sánchez-Ortega.∗ This paper is an expanded version of the lecture notes from the author’s talk at the Second International Workshop on Polynomial Identities, 2–6 September 2011, which took place at the Atlantic Algebra Centre, Memorial University, St. John’s, Newfoundland, Canada.},
author = {R. Bremner, Murray},
journal = {Serdica Mathematical Journal},
keywords = {Algebras; Triple Systems; Dialgebras; Triple Disystems; Polynomial Identities; Multilinear Operations; Computer Algebra},
language = {eng},
number = {1-3},
pages = {91-136},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Algebras, Dialgebras, and Polynomial Identities},
url = {http://eudml.org/doc/288276},
volume = {38},
year = {2012},
}

TY - JOUR
AU - R. Bremner, Murray
TI - Algebras, Dialgebras, and Polynomial Identities
JO - Serdica Mathematical Journal
PY - 2012
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 38
IS - 1-3
SP - 91
EP - 136
AB - 2010 Mathematics Subject Classification: Primary 17A30. Secondary 16R10, 17-08, 17A32,This is a survey of some recent developments in the theory of associative and nonassociative dialgebras, with an emphasis on polynomial identities and multilinear operations. We discuss associative, Lie, Jordan, and alternative algebras, and the corresponding dialgebras; the KP algorithm for converting identities for algebras into identities for dialgebras; the BSO algorithm for converting operations in algebras into operations in dialgebras; Lie and Jordan triple systems, and the corresponding disystems; and a noncommutative version of Lie triple systems based on the trilinear operation abc − bca. The paper concludes with a conjecture relating the KP and BSO algorithms, and some suggestions for further research. Most of the original results are joint work with Raúl Felipe, Luiz A. Peresi, and Juana Sánchez-Ortega.∗ This paper is an expanded version of the lecture notes from the author’s talk at the Second International Workshop on Polynomial Identities, 2–6 September 2011, which took place at the Atlantic Algebra Centre, Memorial University, St. John’s, Newfoundland, Canada.
LA - eng
KW - Algebras; Triple Systems; Dialgebras; Triple Disystems; Polynomial Identities; Multilinear Operations; Computer Algebra
UR - http://eudml.org/doc/288276
ER -