We associate a deformation of the Heisenberg algebra with the suitably normalized Yang R-matrix, and we investigate its properties. Moreover, we construct new examples of quantum vertex algebras, which possess the same representation theory as the aforementioned deformed Heisenberg algebra.
REFERENCES
1.
A. A.
Belavin
, A. M.
Polyakov
, and A. B.
Zamolodchikov
, “Infinite conformal symmetry in two-dimensional quantum field theory
,” Nucl. Phys. B
241
, 333
–380
(1984
).2.
R. E.
Borcherds
, “Vertex algebras, Kac–Moody algebras, and the monster
,” Proc. Natl. Acad. Sci. U. S. A.
83
, 3068
–3071
(1986
).3.
A.
De Sole
, M.
Gardini
, and V. G.
Kac
, “On the structure of quantum vertex algebras
,” J. Math. Phys.
61
, 011701
(2020
); arXiv:1906.05051 [math.QA].4.
P.
Etingof
and D.
Kazhdan
, “Quantization of Lie bialgebras, V
,” Sel. Math.
6
, 105
–130
(2000
); arXiv:math/9808121 [math.QA].5.
E.
Frenkel
and D.
Ben-Zvi
, Vertex Algebras, Algebraic Curves
, 2nd ed., Mathematical Surveys and Monographs Vol. 88 (American Mathematical Society
, Providence, RI
, 2004
).6.
I. B.
Frenkel
and V. G.
Kac
, “Basic representations of affine Lie algebras and dual resonance models
,” Invent. Math.
62
, 23
–66
(1980
).7.
I.
Frenkel
, J.
Lepowsky
, and A.
Meurman
, Vertex Operator Algebras and the Monster
, Pure and Applied Mathematics Vol. 134 (Academic Press, Inc.
, Boston, MA
, 1988
).8.
I. B.
Frenkel
and Y.
Zhu
, “Vertex operator algebras associated to representations of affine and Virasoro algebras
,” Duke Math. J.
66
, 123
–168
(1992
).9.
V.
Kac
, Vertex Algebras for Beginners
, University Lecture Series Vol. 10 (American Mathematical Society
, Providence, RI
, 1997
).10.
C.
Kassel
, Quantum Groups
, Graduate Texts in Mathematics Vol. 155 (Springer-Verlag
, 1995
).11.
S.
Kožić
, “Quantum current algebras associated with rational R-matrix
,” Adv. Math.
351
, 1072
–1104
(2019
); arXiv:1801.03543 [math.QA].12.
J.
Lepowsky
and H.-S.
Li
, Introduction to Vertex Operator Algebras and Their Representations
, Progress in Mathematics Vol. 227 (Birkhäuser
, Boston
, 2003
).13.
J.
Lepowsky
and R. L.
Wilson
, “Construction of the affine Lie algebra
,” Commun. Math. Phys.
62
, 43
–53
(1978
).14.
H.
Li
, “ℏ-adic quantum vertex algebras and their modules
,” Commun. Math. Phys.
296
, 475
–523
(2010
); arXiv:0812.3156 [math.QA].15.
H.
Li
, “Associating quantum vertex algebras to deformed Heisenberg Lie algebras
,” Front. Math. China
6
, 707
–730
(2011
); arXiv:1106.3241 [math.QA].16.
B. H.
Lian
, “On the classification of simple vertex operator algebras
,” Commun. Math. Phys.
163
, 307
–357
(1994
).17.
N. Y.
Reshetikhin
and M. A.
Semenov-Tian-Shansky
, “Central extensions of quantum current groups
,” Lett. Math. Phys.
19
, 133
–142
(1990
).18.
G.
Segal
, “Unitary representations of some infinite-dimensional groups
,” Commun. Math. Phys.
80
, 301
–342
(1981
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.