scholarly journals Another construction of the central extension of the loop group

1988 ◽  
Vol 116 (1) ◽  
pp. 73-80 ◽  
Author(s):  
M. K. Murray
Keyword(s):  
Central Extension ◽  
Loop Group

scholarly journals Coadjoint Orbits, Cocycles and Gravitational Wess–Zumino

2018 ◽  
Vol 30 (06) ◽  
pp. 1840001 ◽  
Author(s):  
Anton Alekseev ◽  
Samson L. Shatashvili
Keyword(s):  
Path Integral ◽  
Central Extension ◽  
General Feature ◽  
Integral Formula ◽  
Loop Group ◽  
Boundary Term ◽  
Coadjoint Orbits ◽  
Joint Work ◽  
Cocycle Property ◽  
Geometric Action

About 30 years ago, in a joint work with L. Faddeev we introduced a geometric action on coadjoint orbits. This action, in particular, gives rise to a path integral formula for characters of the corresponding group [Formula: see text]. In this paper, we revisit this topic and observe that the geometric action is a 1-cocycle for the loop group [Formula: see text]. In the case of [Formula: see text] being a central extension, we construct Wess–Zumino (WZ) type terms and show that the cocycle property of the geometric action gives rise to a Polyakov–Wiegmann (PW) formula with boundary term given by the 2-cocycle which defines the central extension. In particular, we obtain a PW type formula for Polyakov’s gravitational WZ action. After quantization, this formula leads to an interesting bulk-boundary decoupling phenomenon previously observed in the WZW model. We explain that this decoupling is a general feature of the Wess–Zumino terms obtained from geometric actions, and that in this case, the path integral is expressed in terms of the 2-cocycle which defines the central extension. In memory of our teacher Ludwig Faddeev

SUPERGRAVITY AND SUPERSTRINGS IN (2+1) DIMENSIONS

1991 ◽  
Vol 06 (29) ◽  
pp. 5215-5229 ◽  
Author(s):  
A. STERN
Keyword(s):  
Minkowski Space ◽  
Current Algebra ◽  
Central Extension ◽  
Loop Group ◽  
Unitary Representations ◽  
Two Dimensional ◽  
Induced Representations ◽  
Highest Weight ◽  
Dimensional Minkowski Space ◽  
State Construction

We study n=1 supergravity written on a two-dimensional disc (× time) in the absence of any sources. The dynamics of the boundary of the disc is equivalent to that of a superstring in (2+1)-dimensional Minkowski space. The relevant current algebra for the theory corresponds to the central extension of the super-Poincaré loop group. We find unitary representations of the current algebra by applying both a highest weight state construction and the method of induced representations.

FUNCTIONAL DIFFERENTIAL REALIZATION OF THE KAC–MOODY ALGEBRA AND GROUP COHOMOLOGY

1991 ◽  
Vol 06 (31) ◽  
pp. 2881-2885
Author(s):  
B. E. BAAQUIE
Keyword(s):  
Central Extension ◽  
Loop Group ◽  
Group Cohomology ◽  
Exact Expression ◽  
Moody Algebra ◽  
Functional Differential

The Kac–Moody generators are realized as the central extension of the loop group generators. The exact expression for the central extension is obtained from the Wess–Zumino zero-cochain density via the descent equations of group cohomology.

scholarly journals On the vanishing problem of string classes

1996 ◽  
Vol 61 (2) ◽  
pp. 258-266 ◽  
Author(s):  
Katsuhiko Kuribayashi
Keyword(s):  
Central Extension ◽  
Loop Group ◽  
Ring Structure ◽  
Structure Group ◽  
Universal Central Extension ◽  
String Class ◽  
String Classes

AbstractThe ordinary string class is an obstruction to lift the structure group LSpin(n) of a loop group bundle LQ → LM to the universal central extension of LSpin(n) by the circle. The vanishing problem of the ordinary string class and generalized string classes are considered from the viewpoint of the ring structure of the cohomology H*(M; R).

scholarly journals A unitary representation of the basical central extension of a loop group

2000 ◽  
Vol 159 ◽  
pp. 113-124 ◽  
Author(s):  
Rémi Léandre
Keyword(s):  
Riemannian Manifold ◽  
Unitary Representation ◽  
Central Extension ◽  
Loop Space ◽  
Finite Energy ◽  
Loop Group

We construct a measure over the string bundle associated to the loop space of a Riemannian manifold. We deduce a representation of a finite energy Kac-Moody group analoguous to the energy representation.

scholarly journals Comparison of the clinical outcomes of skin bridge loop ileostomy and traditional loop ileostomy in patients with low rectal cancer

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hui Ye ◽  
Shujuan Huang ◽  
Jie Yu ◽  
Qichang Zhou ◽  
Changlei Xi ◽  
...  
Keyword(s):  
Rectal Cancer ◽  
Low Anterior Resection ◽  
Clinical Evidence ◽  
Loop Ileostomy ◽  
Loop Group ◽  
Clinical Results ◽  
Low Rectal Cancer ◽  
Analog Scale ◽  
Traditional Group ◽  
Bridge Group

AbstractTo compare the clinical results of patients with low rectal cancer who underwent skin bridge loop ileostomy and traditional loop ileostomy, and provide clinical evidence for choosing a better ostomy method. We retrospectively collected data of 118 patients with rectal cancer who underwent low anterior resection and loop ileostomy. To investigate the patients characteristics, postoperative stoma-related complications and the frequency of exchanged ostomy bags. The differences of these indicators between the two groups of patients who underwent skin bridge loop ileostomy and traditional loop ileostomy were compared. The Visual Analog Scale (VAS) score of the skin bridge loop ileostomy group was lower than that of the traditional ileostomy loop group (P < 0.05). The skin bridge group had a lower Discoloration, Erosion, Tissue overgrowth (DET) score and incidence of mucocutaneous separation than the traditional group at the 1st and 2nd weeks after operation (P < 0.05). The average number of weekly exchanged ostomy bags was significantly less in the skin bridge group than in the traditional group within 4 weeks after surgery (P < 0.05). Our experience demonstrates that the skin bridge loop ileostomy may significantly reduce early postoperative stoma-related complications, the frequency of exchanged ostomy bags and patients’ medical costs after discharge.

Sign in / Sign up

Export Citation Format

Share Document