Zobrazeno 1 - 10
of 44
pro vyhledávání: '"Andrew James Bruce"'
Autor:
Andrew James Bruce
Publikováno v:
Symmetry, Vol 16, Iss 6, p 725 (2024)
We examine the heap of linear connections on anchored vector bundles and Lie algebroids. Naturally, this covers the example of affine connections on a manifold. We present some new interpretations of classical results via this ternary structure of co
Externí odkaz:
https://doaj.org/article/4833ef624a304095a1f8f68c5c56fddf
Autor:
Andrew James Bruce
Publikováno v:
Nuclear Physics B, Vol 971, Iss , Pp 115514- (2021)
We examine the question of the integrability of the recently defined Z2×Z2-graded sine-Gordon model, which is a natural generalisation of the supersymmetric sine-Gordon equation. We do this via appropriate auto-Bäcklund transformations, constructio
Externí odkaz:
https://doaj.org/article/fb94a478392645b69adf0d31afb9136a
Autor:
Andrew James Bruce
Publikováno v:
Universe, Vol 8, Iss 1, p 56 (2022)
We re-examine the appearance of semiheaps and (para-associative) ternary algebras in quantum mechanics. In particular, we review the construction of a semiheap on a Hilbert space and the set of bounded operators on a Hilbert space. The new aspect of
Externí odkaz:
https://doaj.org/article/0f45785c3ca5498f9cbb03fd67e92d65
Autor:
Andrew James Bruce, Janusz Grabowski
Publikováno v:
Mathematics, Vol 8, Iss 9, p 1469 (2020)
Very loosely, Z2n-manifolds are ‘manifolds’ with Z2n-graded coordinates and their sign rule is determined by the scalar product of their Z2n-degrees. A little more carefully, such objects can be understood within a sheaf-theoretical framework, ju
Externí odkaz:
https://doaj.org/article/3b124af2ae834664aa9a7b4c795d1168
Autor:
Andrew James Bruce
Publikováno v:
Symmetry, Vol 11, Iss 1, p 116 (2019)
We extend the notion of super-Minkowski space-time to include Z 2 n -graded (Majorana) spinor coordinates. Our choice of the grading leads to spinor coordinates that are nilpotent but commute amongst themselves. The mathematical framework we employ i
Externí odkaz:
https://doaj.org/article/cd8cb6746ecc4e6aaf94715800977e06
Autor:
Andrew James Bruce
Publikováno v:
Journal of Mathematics, Vol 2014 (2014)
We construct a nonskew symmetric version of a Poisson bracket on the algebra of smooth functions on an odd Jacobi supermanifold. We refer to such Poisson-like brackets as Loday-Poisson brackets. We examine the relations between the Hamiltonian vector
Externí odkaz:
https://doaj.org/article/86252e433d4b41f48d0eac152ef43e14
Autor:
Steven Duplij, Andrew James Bruce
Publikováno v:
Reports on Mathematical Physics. 86:383-400
A $\mathbb{Z}_2 \times \mathbb{Z}_2$-graded generalisation of the quantum superplane is proposed and studied. We construct a bicovariant calculus on what we shall refer to as the \emph{double-graded quantum superplane}. The commutation rules between
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f08aa420817c658ba3d4d4eac00f176e
https://doi.org/10.1016/s0034-4877(20)30089-6
https://doi.org/10.1016/s0034-4877(20)30089-6
Autor:
Janusz Grabowski, Andrew James Bruce
Publikováno v:
Journal of Geometry and Physics. 142:254-273
Pre-Courant algebroids are `Courant algebroids' without the Jacobi identity for the Courant-Dorfman bracket. In this paper we examine the corresponding supermanifold description of pre-Courant algebroids and some direct consequences thereof - such as
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4347b22f5bc8bada7d0bb8c5615d3499
https://doi.org/10.1016/j.geomphys.2019.04.007
https://doi.org/10.1016/j.geomphys.2019.04.007
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications.
We establish the representability of the general linear ${\mathbb Z}_2^n$-group and use the restricted functor of points - whose test category is the category of ${\mathbb Z}_2^n$-manifolds over a single topological point - to define its smooth linea
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d80c73c52d978ad47ea7ad17ed05eaad
https://doi.org/10.3842/sigma.2021.060
https://doi.org/10.3842/sigma.2021.060
Autor:
Janusz Grabowski, Andrew James Bruce
Roughly speaking, $\mathbb{Z}_2^n$-manifolds are `manifolds' equipped with $\mathbb{Z}_2^n$-graded commutative coordinates with the sign rule being determined by the scalar product of their $\mathbb{Z}_2^n$-degrees. We examine the notion of a symplec
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::52707bae43d0706fe45cd1557415efda
http://arxiv.org/abs/2103.00249
http://arxiv.org/abs/2103.00249
