Abstract
The concept of an algebra being hom-associative is examined, and found to allow some awkward complications. A modified concept of strong hom-associativity is introduced to eliminate those quirks. It is proved that the basic “Yau twist” construction of a hom-associative algebra from an associative algebra does in fact produce strongly hom-associative algebras. It is proved that the axioms for a strongly hom-associative algebra yields a confluent rewrite system, and a basis for the free strongly hom-associative algebra is given a finite presentation through a parsing expression grammar.
Keywords
MSC 2010 Classification:
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Lugiez, D., Löding, C., Tison, S., Tommasi, M.: Tree Automata Techniques and Applications (web book), version of November 18, 2008. http://tata.gforge.inria.fr/
Ford, B.: Parsing expression grammars: a recognition-based syntactic foundation. In: Jones, N.D., Leroy, X. (eds.) Proceedings of the 31st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2004, Venice, Italy, January 14–16, 111–122. ACM (2004)
Guo, L., Zhang, B., Zheng, S.: Universal enveloping algebras and Poincaré-Birkhoff-Witt theorem for involutive Hom-Lie algebras. J. Lie Theory 28(3), 739–759 (2018)
Hartwig, J.T., Larsson, D., Silvestrov, S.D.: Deformations of Lie algebras using \(\sigma \)-derivations. J. Algebra 295, 314–361 (2006)
Hellström, L., Makhlouf, A., Silvestrov, S.D.: Universal algebra applied to hom-associative algebras, and more. In: Makhlouf, A., Paal, E., Silvestrov, S., Stolin, A. (eds.), Algebra, Geometry and Mathematical Physics, Springer Proceedings in Mathematics and Statistics, vol. 85, 157–199 (2014)
International Standards Organization. Syntactic metalanguage – Extended BNF, 1996. ISO/IEC 14977
Lee, L.: Fast context-free grammar parsing requires fast Boolean matrix multiplication. J. ACM 49(1), 1–15 (2002)
Lyndon, R.C.: On Burnside’s problem. Trans. Am. Math. Soc. 77, 202–215 (1954)
Makhlouf, A., Silvestrov, S.D.: Hom-algebra structures. J. Gen. Lie Theory Appl. 2(No. 2), 51–64 (2008)
Shirshov, A.I.: Subalgebras of free Lie algebras. (Russian) Mat. Sbornik N.S. 33(75), 441–452 (1953)
Shirshov, A.I.: Some algorithm problems for Lie algebras. (Russian) Sibirsk. Mat. Ž. 3, 292–296 (1962)
Yau, D.: Enveloping algebra of Hom-Lie algebras. J. Gen. Lie Theory Appl. 2, 95–108 (2008)
Zheng, S., Guo, L.: Free involutive Hom-semigroups and Hom-associative algebras. Front. Math. China 11(2), 497–508 (2016)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Hellström, L. (2020). Strong Hom-Associativity. In: Silvestrov, S., Malyarenko, A., Rančić, M. (eds) Algebraic Structures and Applications. SPAS 2017. Springer Proceedings in Mathematics & Statistics, vol 317. Springer, Cham. https://doi.org/10.1007/978-3-030-41850-2_12
Download citation
DOI: https://doi.org/10.1007/978-3-030-41850-2_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-41849-6
Online ISBN: 978-3-030-41850-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)