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pro vyhledávání: '"McInroy, Justin"'
Autor:
McInroy, Justin, Shpectorov, Sergey
Axial algebras are a class of non-associative commutative algebras whose properties are defined in terms of a fusion law. When this fusion law is graded, the algebra has a naturally associated group of automorphisms and thus axial algebras are inhere
Externí odkaz:
http://arxiv.org/abs/2209.08043
Axial algebras are a class of non-associative algebra with a strong link to finite (especially simple) groups which have recently received much attention. Of primary interest are the axial algebras of Monster type $(\alpha, \beta)$, of which the Grie
Externí odkaz:
http://arxiv.org/abs/2205.02200
Autor:
McInroy, Justin, Shpectorov, Sergey
Ivanov introduced the shape of a Majorana algebra as a record of the $2$-generated subalgebras arising in that algebra. As a broad generalisation of this concept and to free it from the ambient algebra, we introduce the concept of an axet and shapes
Externí odkaz:
http://arxiv.org/abs/2107.07415
Autor:
McInroy, Justin
Axial algebras are a recently introduced class of non-associative algebra, with a naturally associated group, which generalise the Griess algebra and some key features of the moonshine VOA. Sakuma's Theorem classifies the eight $2$-generated axial al
Externí odkaz:
http://arxiv.org/abs/2004.11773
Publikováno v:
Journal of Pure and Applied Algebra 225, 2021
A code algebra $A_C$ is a nonassociative commutative algebra defined via a binary linear code $C$. In a previous paper, we classified when code algebras are $\mathbb{Z}_2$-graded axial (decomposition) algebras generated by small idempotents. In this
Externí odkaz:
http://arxiv.org/abs/2001.08426
An axial algebra is a commutative non-associative algebra generated by axes, that is, primitive, semisimple idempotents whose eigenvectors multiply according to a certain fusion law. The Griess algebra, whose automorphism group is the Monster, is an
Externí odkaz:
http://arxiv.org/abs/1809.10657
Publikováno v:
Trans. Amer. Math. Soc. 373 (2020), 2135-2156
Axial algebras are a recently introduced class of non-associative algebra motivated by applications to groups and vertex-operator algebras. We develop the structure theory of axial algebras focussing on two major topics: (1) radical and simplicity; a
Externí odkaz:
http://arxiv.org/abs/1809.10132
Autor:
McInroy, Justin, Shpectorov, Sergey
Publikováno v:
J. Algebra 550 (2020), 379-409
An axial algebra $A$ is a commutative non-associative algebra generated by primitive idempotents, called axes, whose adjoint action on $A$ is semisimple and multiplication of eigenvectors is controlled by a certain fusion law. Different fusion laws d
Externí odkaz:
http://arxiv.org/abs/1804.00587
Publikováno v:
Israel J. Math., 233, no. 1, 401-438 (2019)
A code algebra $A_C$ is a non-associative commutative algebra defined via a binary linear code $C$. We study certain idempotents in code algebras, which we call small idempotents, that are determined by a single non-zero codeword. For a general code
Externí odkaz:
http://arxiv.org/abs/1802.03342
Publikováno v:
J. Algebra 518, 146-176 (2019)
Inspired by code vertex operator algebras (VOAs) and their representation theory, we define code algebras, a new class of commutative non-associative algebras constructed from binary linear codes. Let $C$ be a binary linear code of length $n$. A basi
Externí odkaz:
http://arxiv.org/abs/1707.07992