Zobrazeno 1 - 10
of 24
pro vyhledávání: '"53D55, 81R60"'
Autor:
Okuda, Taika, Sako, Akifumi
We construct the deformation quantization with separation of variables on the Grassmannian $G_{2,4}\left(\mathbb{C}\right)$. The star product on $G_{2,4}\left(\mathbb{C}\right)$ can be explicitly determined as the solution of the recurrence relations
Externí odkaz:
http://arxiv.org/abs/2401.00500
Autor:
Zhao, Hu
Given a finite quiver, its double may be viewed as its non-commutative "cotangent" space, and hence is a non-commutative symplectic space. Crawley-Boevey, Etingof and Ginzburg constructed the non-commutative reduction of this space while Schedler con
Externí odkaz:
http://arxiv.org/abs/2105.05440
Publikováno v:
Algebr. Geom. Topol. 23 (2023) 339-418
Quantization of the Teichm\"uller space of a punctured Riemann surface $S$ is an approach to $3$-dimensional quantum gravity, and is a prototypical example of quantization of cluster varieties. Any simple loop $\gamma$ in $S$ gives rise to a natural
Externí odkaz:
http://arxiv.org/abs/1812.11628
Autor:
Hara, Kentaro, Sako, Akifumi
We derive algebraic recurrence relations to obtain a deformation quantization with separation of variables for a locally symmetric K\"ahler manifold. This quantization method is one of the ways to perform a deformation quantization of K\"ahler manifo
Externí odkaz:
http://arxiv.org/abs/1608.08146
Publikováno v:
Letters in Mathematical Physics, 107(9), 1591-1628 (2017)
We develop a sheaf theory approach to toric noncommutative geometry which allows us to formalize the concept of mapping spaces between two toric noncommutative spaces. As an application we study the `internalized' automorphism group of a toric noncom
Externí odkaz:
http://arxiv.org/abs/1606.04775
Autor:
Sako, Akifumi, Umetsu, Hiroshi
We introduce twisted Fock representations of noncommutative K\"ahler manifolds and give their explicit expressions. The twisted Fock representation is a representation of the Heisenberg like algebra whose states are constructed by acting creation ope
Externí odkaz:
http://arxiv.org/abs/1605.02600
We give the Fock representation of a noncommutative $\mathbb{C}P^N$ and gauge theories on it. The Fock representation is constructed based on star products given by deformation quantization with separation of variables and operators which act on stat
Externí odkaz:
http://arxiv.org/abs/1506.06957
We construct a gauge theory on a noncommutative homogeneous K\"ahler manifold, where we employ the deformation quantization with separation of variables for K\"ahler manifolds formulated by Karabegov. A key point in this construction is to obtaining
Externí odkaz:
http://arxiv.org/abs/1403.5727
Autor:
Aschieri, Paolo
Publikováno v:
Int. Jou. Mod. Phys. Conf. Ser. 13 (2012) 1-19
Given a Hopf algebra H and an algebra A that is an H-module algebra we consider the category of left H-modules and A-bimodules, where morphisms are just right A-linear maps (not necessarily H-equivariant). Given a twist F of H we then quantize (defor
Externí odkaz:
http://arxiv.org/abs/1210.1143
Autor:
Aschieri, Paolo, Schenkel, Alexander
Publikováno v:
Adv. Theor. Math. Phys. 18 3 (2014) 513-612
Given a Hopf algebra H, we study modules and bimodules over an algebra A that carry an H-action, as well as their morphisms and connections. Bimodules naturally arise when considering noncommutative analogues of tensor bundles. For quasitriangular Ho
Externí odkaz:
http://arxiv.org/abs/1210.0241