IRIS Università degli Studi di Padovahttps://www.research.unipd.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Wed, 11 Dec 2019 01:07:17 GMT2019-12-11T01:07:17Z1041- Centralisers in Classical Lie algebrashttp://hdl.handle.net/11577/3071299Titolo: Centralisers in Classical Lie algebras
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11577/30712992014-01-01T00:00:00Z
- Invariants of centralisers in positive characteristichttp://hdl.handle.net/11577/3070899Titolo: Invariants of centralisers in positive characteristic
Abstract: Let Q be a simple algebraic group of type A or C over a field of good positive characteristic. Let x∈q=Lie(Q) and consider the centraliser qx={y∈q:[xy]=0}. We show that the invariant algebra S(qx)^{qx} is generated by the p th power subalgebra and the mod p reduction of the characteristic zero invariant algebra. The latter algebra is known to be polynomial and we show that it remains so after reduction. Using a theory of symmetrisation in positive characteristic we prove the analogue of this result in the enveloping algebra, where the p -centre plays the role of the p th power subalgebra. In Zassenhausʼ foundational work, the invariant theory and representation theory of modular Lie algebras were shown to be explicitly intertwined. We exploit his theory to give a precise upper bound for the dimensions of simple qx-modules. An application to the geometry of the Zassenhaus variety is given.
When g is of type A and g=k⊕p is a symmetric decomposition of orthogonal type we use similar methods to show that for every nilpotent e∈k the invariant algebra S(pe)^{ke} is generated by the p th power subalgebra and S(pe)^{Ke} which is also shown to be polynomial.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11577/30708992014-01-01T00:00:00Z
- Derived subalgebras of centralisers and finite -algebrashttp://hdl.handle.net/11577/3071099Titolo: Derived subalgebras of centralisers and finite -algebras
Abstract: Let g=Lie(G) be the Lie algebra of a simple algebraic group G over an algebraically closed field of characteristic 0. Let e be a nilpotent element of g and let ge=Lie(Ge) where Ge stands for the stabiliser of e in G. For g classical, we give an explicit combinatorial formula for the codimension of [ge,ge] in ge and use it to determine those e∈g for which the largest commutative quotient U(g,e)^{ab} of the finite W-algebra U(g,e) is isomorphic to a polynomial algebra. It turns out that this happens if and only if e lies in a unique sheet of g. The nilpotent elements with this property are called non-singular in the paper. Confirming a recent conjecture of Izosimov, we prove that a nilpotent element e∈g is non-singular if and only if the maximal dimension of the geometric quotients S/G, where S is a sheet of g containing e, coincides with the codimension of [ge,ge] in ge and describe all non-singular nilpotent elements in terms of partitions. We also show that for any nilpotent element e in a classical Lie algebra g the closed subset of Specm U(g,e)^{ab} consisting of all points fixed by the natural action of the component group of Ge is isomorphic to an affine space. Analogues of these results for exceptional Lie algebras are also obtained and applications to the theory of primitive ideals are given.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11577/30710992014-01-01T00:00:00Z
- International Variation in Surgical Practices in Units Performing Oesophagectomy for Oesophageal Cancer: A Unit Survey from the Oesophago-Gastric Anastomosis Audit (OGAA)http://hdl.handle.net/11577/3307085Titolo: International Variation in Surgical Practices in Units Performing Oesophagectomy for Oesophageal Cancer: A Unit Survey from the Oesophago-Gastric Anastomosis Audit (OGAA)
Abstract: Background: Anastomotic leaks are associated with significant risk of morbidity, mortality and treatment costs after oesophagectomy. The aim of this study was to evaluate international variation in unit-level clinical practice and resource availability for the prevention and management of anastomotic leak following oesophagectomy. Method: The Oesophago-Gastric Anastomosis Audit (OGAA) is an international research collaboration focussed on improving the care and outcomes of patients undergoing oesophagectomy. Any unit performing oesophagectomy worldwide can register to participate in OGAA studies. An online unit survey was developed and disseminated to lead surgeons at each unit registered to participate in OGAA. High-income country (HIC) and low/middle-income country (LMIC) were defined according to the World Bank whilst unit volume were defined as < 20 versus 20–59 versus ≥60 cases/year in the unit. Results: Responses were received from 141 units, a 77% (141/182) response rate. Median annual oesophagectomy caseload was reported to be 26 (inter-quartile range 12–50). Only 48% (68/141) and 22% (31/141) of units had an Enhanced Recovery After Surgery (ERAS) program and ERAS nurse, respectively. HIC units had significantly higher rates of stapled anastomosis compared to LMIC units (66 vs 31%, p = 0.005). Routine post-operative contrast-swallow anastomotic assessment was performed in 52% (73/141) units. Stent placement and interventional radiology drainage for anastomotic leak management were more commonly available in HICs than LMICs (99 vs 59%, p < 0.001 and 99 vs 83%, p < 0.001). Conclusions: This international survey highlighted variation in surgical technique and management of anastomotic leak based on case volume and country income level. Further research is needed to understand the impact of this variation on patient outcomes. © 2019, Société Internationale de Chirurgie.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/11577/33070852019-01-01T00:00:00Z