Orders of Torsion Units of integral reality-based algebras with rational multiplicities

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dc.contributor.authorHerman, Allen
dc.contributor.authorSingh, Gurmail
dc.date.accessioned2021-09-14T01:09:49Z
dc.date.available2021-09-14T01:09:49Z
dc.date.issued2018
dc.description.abstractA reality-based algebra (RBA) is a finite-dimensional associative algebra with involution over C whose distinguished basis B contains 1 and is closed under pseudo-inverse. An integral RBA is one whose structure constants in its distinguished basis are integers. If the algebra has a one-dimensional representation taking positive values on B, then we say that the RBA has a positive degree map. These RBAs have a standard feasible trace, and the multiplicities of the irreducible characters in the standard feasible trace are the multiplicities of the RBA. In this paper, we show that for integral RBAs with positive degree map whose multiplicities are rational, any finite subgroup of torsion units whose elements are all of degree 1 and have algebraic integer coefficients must have order dividing a certain positive integer determined by the degree map and the multiplicities. The paper concludes with a thorough investigation of the properties of RBAs that force multiplicities to be rational.en_US
dc.description.authorstatusFacultyen_US
dc.description.peerreviewyesen_US
dc.description.sponsorshipNSERC Discovery Grant, RGPIN-2017-05331en_US
dc.identifier.citationJournal of Algebra and its Applications, Vol. 17, No. 1, 1850015 (12 pages)en_US
dc.identifier.doi10.1142/S0219498818500159
dc.identifier.urihttps://hdl.handle.net/10294/12316
dc.subjectReality-based algebras, table algebras, fusion algebras, group of units, torsion units,multiplicitiesen_US
dc.titleOrders of Torsion Units of integral reality-based algebras with rational multiplicitiesen_US
dc.typeArticleen_US
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