The relative canonical algebra for genus 4 fibrations

1995 ◽  
Vol 11 (1) ◽  
pp. 44-52 ◽  
Author(s):  
Cai Jinxing
Keyword(s):  
Canonical Algebra

scholarly journals Kac Polynomials for Canonical Algebras

2017 ◽  
Vol 2019 (13) ◽  
pp. 3981-4003
Author(s):  
Pierre-Guy Plamondon ◽  
Olivier Schiffmann
Keyword(s):  
Finite Field ◽  
Dimension Vector ◽  
Indecomposable Representations ◽  
Moduli Stacks ◽  
Fixed Dimension ◽  
Canonical Algebra

Abstract We prove that the number of geometrically indecomposable representations of fixed dimension vector $\mathbf{d}$ of a canonical algebra $C$ defined over a finite field $\mathbb{F}_q$ is given by a polynomial in $q$ (depending on $C$ and $\mathbf{d}$). We prove a similar result for squid algebras. Finally, we express the volume of the moduli stacks of representations of these algebras of a fixed dimension vector in terms of the corresponding Kac polynomials.

scholarly journals The cluster category of a canonical algebra

2010 ◽  
Vol 362 (08) ◽  
pp. 4313-4330 ◽  
Author(s):  
M. Barot ◽  
D. Kussin ◽  
H. Lenzing
Keyword(s):  
Cluster Category ◽  
Canonical Algebra

INFORMATION GEOMETRY FOR SOME LIE ALGEBRAS

1999 ◽  
Vol 02 (03) ◽  
pp. 441-460 ◽  
Author(s):  
H. NENCKA ◽  
R. F. STREATER
Keyword(s):  
Lie Algebras ◽  
Discrete Series ◽  
Complex Structure ◽  
Solvable Model ◽  
Coadjoint Orbits ◽  
Exactly Solvable Model ◽  
Metaplectic Representation ◽  
Canonical Algebra ◽  
Model Dynamics ◽  
Exactly Solvable

For certain unitary representations of a Lie algebra [Formula: see text] we define the statistical manifold ℳ of states as the convex cone of [Formula: see text] for which the partition function Z= Tr exp {-X} is finite. The Hessian of Ψ= log Z defines a Riemannian metric g on [Formula: see text], (the Bogoliubov–Kubo–Mori metric); [Formula: see text] foliates into the union of coadjoint orbits, each of which can be given a complex structure (that of Kostant). The program is carried out for so(3), and for sl(2,R) in the discrete series. We show that ℳ=R+× CP 1 and R+×H respectively. We show that for the metaplectic representation of the quadratic canonical algebra, ℳ=R+× CP 2/Z2. Exactly solvable model dynamics is constructed in each case.

scholarly journals ELECTRIC-MAGNETIC DUALITY AND THE “LOOP REPRESENTATION” IN ABELIAN GAUGE THEORIES

1996 ◽  
Vol 11 (13) ◽  
pp. 1107-1114 ◽  
Author(s):  
LORENZO LEAL
Keyword(s):  
Phase Space ◽  
Gauge Theories ◽  
Topological Algebra ◽  
Geometric Representation ◽  
Abelian Gauge ◽  
Dual Algebra ◽  
Nonlocal Operators ◽  
Canonical Algebra

Abelian gauge theories are quantized in a geometric representation that generalizes the loop representation and treats electric and magnetic operators on the same footing. The usual canonical algebra is turned into a topological algebra of nonlocal operators that resembles the order-disorder dual algebra of ’t Hooft. These dual operators provide a complete description of the physical phase space of the theories.

Canonical algebra of GL(4)-invariant gravity

1990 ◽  
Vol 7 (6) ◽  
pp. 975-984 ◽  
Author(s):  
R Floreanini ◽  
R Percacci
Keyword(s):  
Canonical Algebra

scholarly journals Examples of bad noetherian local rings

1978 ◽  
Vol 70 ◽  
pp. 105-110 ◽  
Author(s):  
Maria Grazia Marinari
Keyword(s):  
Noetherian Rings ◽  
Local Rings ◽  
General Technique ◽  
Canonical Module ◽  
Gorenstein Rings ◽  
Canonical Algebra ◽  
Regular Local Rings

In this paper we use a general technique, due to Larfeldt-Lech [9], to show that there exist local noetherian rings which are “bad” with respect to some properties which are obviously verified in the algebro-geometric case. In particular we show that there exist local Gorenstein rings which are not homomorphic images of regular (local) rings and that there exist local rings which do have canonical module but do not have canonical algebra.

THE CANONICAL ALGEBRA OF SYMMETRIES FOR GAUGE THEORIES: THE EXAMPLE OF ANYONS

1994 ◽  
Vol 09 (31) ◽  
pp. 2903-2912
Author(s):  
J. M. PONS
Keyword(s):  
Gauge Theories ◽  
Canonical Formalism ◽  
Symmetry Algebra ◽  
Ideal Gas ◽  
Constrained Systems ◽  
Canonical Algebra ◽  
Constants Of Motion ◽  
Symmetry Generators ◽  
Continuous Symmetries

Some special features of the algebra of continuous symmetries for constrained systems are illustrated through the example of the nonrelativistic ideal gas of anyons. The relation between constants of motion and symmetry generators for this gauge system is completely worked out. The generators of both its rigid and gauge continuous symmetries are explicitly given in the canonical formalism. Also the interplay between these two types of symmetries within the symmetry algebra is exhibited.

scholarly journals A Canonical Algebra of Open Transition Systems

2021 ◽  
pp. 63-81
Author(s):  
Elena Di Lavore ◽  
Alessandro Gianola ◽  
Mario Román ◽  
Nicoletta Sabadini ◽  
Paweł Sobociński
Keyword(s):  
Transition Systems ◽  
Canonical Algebra

scholarly journals Weighted Projective Lines and Rational Surface Singularities

2020 ◽  
Vol Volume 3 ◽  
Author(s):  
Osamu Iyama ◽  
Michael Wemyss
Keyword(s):  
Rational Surface ◽  
Projective Line ◽  
Degree Zero ◽  
Dual Graphs ◽  
Canonical Algebra ◽  
Tilting Bundle ◽  
Surface Singularities ◽  
Necessary And Sufficient ◽  
Projective Lines ◽  
Rational Surface Singularities

In this paper we study rational surface singularities R with star shaped dual graphs, and under very mild assumptions on the self-intersection numbers we give an explicit description of all their special Cohen-Macaulay modules. We do this by realising R as a certain Z-graded Veronese subring S^x of the homogeneous coordinate ring S of the Geigle-Lenzing weighted projective line X, and we realise the special CM modules as explicitly described summands of the canonical tilting bundle on X. We then give a second proof that these are special CM modules by comparing qgr S^x and coh X, and we also give a necessary and sufficient combinatorial criterion for these to be equivalent categories. In turn, we show that qgr S^x is equivalent to qgr of the reconstruction algebra, and that the degree zero piece of the reconstruction algebra coincides with Ringel's canonical algebra. This implies that the reconstruction algebra contains the canonical algebra, and furthermore its qgr category is derived equivalent to the canonical algebra, thus linking the reconstruction algebra of rational surface singularities to the canonical algebra of representation theory. Comment: Final version

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