scholarly journals An analogue of a reductive algebraic monoid whose unit group is a Kac-Moody group

2005 ◽  
Vol 174 (823) ◽  
pp. 0-0 ◽  
Author(s):  
Claus Mokler
Keyword(s):  
Unit Group ◽  
Algebraic Monoid

CARTAN SUBMONOIDS OF ALGEBRAIC MONOIDS

1995 ◽  
Vol 05 (03) ◽  
pp. 367-377 ◽  
Author(s):  
WENXUE HUANG
Keyword(s):  
Maximal Torus ◽  
Unit Group ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Completely Regular ◽  
Algebraic Monoid ◽  
Algebraic Monoids

Let M be an irreducible linear algebraic monoid defined over an algebraically closed field K with idempotent set E(M), T a maximal torus of the unit group G of M. We call CM(T)c a Cartan submonoid of M. The following are proved: (1) If M is reductive with zero or completely regular, then CM(T) is irreducible and regular and [Formula: see text]; (2) If M is regular, then M is solvable iff NM(CM(T))=CM(T), in which case, CM(T) is irreducible and regular; (3) If M is regular, then [Formula: see text].

Conjugacy Classes in Algebraic Monoids II

1994 ◽  
Vol 46 (3) ◽  
pp. 648-661 ◽  
Author(s):  
Mohan S. Putcha
Keyword(s):  
Unit Group ◽  
Conjugacy Classes ◽  
Reductive Groups ◽  
Bijective Correspondence ◽  
Twisted Conjugacy ◽  
Algebraic Monoid ◽  
Algebraic Monoids

AbstractLet M be a connected linear algebraic monoid with zero and a reductive unit group. We show that there exist reductive groups G1,..., Gt, each with an automorphism, such that the conjugacy classes of M are in a natural bijective correspondence with the twisted conjugacy classes of Gi, i = 1,..., t.

Affinely spanned quasi-stochastic algebraic monoids

2017 ◽  
Vol 27 (08) ◽  
pp. 1061-1072
Author(s):  
W. Huang ◽  
J. Li
Keyword(s):  
Matrix Element ◽  
Parabolic Subgroup ◽  
Characteristic Zero ◽  
Unit Group ◽  
Initial Study ◽  
Zariski Closure ◽  
Closed Field ◽  
Basic Class ◽  
Algebraic Monoid ◽  
Algebraic Monoids

A linear algebraic monoid over an algebraically closed field [Formula: see text] of characteristic zero is called (row) quasi-stochastic if each row of each matrix element is of sum one. Any linear algebraic monoid over [Formula: see text] can be embedded as an algebraic submonoid of the maximum affinely spanned quasi-stochastic monoid of some degree [Formula: see text]. The affinely spanned quasi-stochastic algebraic monoids form a basic class of quasi-stochastic algebraic monoids. An initial study of structure of affinely spanned quasi-stochastic algebraic monoids is conducted. Among other things, it is proved that the Zariski closure of a parabolic subgroup of the unit group of an affinely spanned quasi-stochastic algebraic monoid is affinely spanned.

scholarly journals Products of idempotents in algebraic monoids

2006 ◽  
Vol 80 (2) ◽  
pp. 193-203 ◽  
Author(s):  
Mohan S. Putcha
Keyword(s):  
Sufficient Conditions ◽  
Unit Group ◽  
Necessary And Sufficient Conditions ◽  
Algebraic Monoid ◽  
Necessary And Sufficient ◽  
Algebraic Monoids

AbstractLet M be a reductive algebraic monoid with zero and unit group G. We obtain a description of the submonoid generated by the idempotents of M. In particular, we find necessary and sufficient conditions for M\G to be idempotent generated.

AN ALGEBRAIC MONOID APPROACH TO LINEAR ASSOCIATIVE ALGEBRAS, II

1996 ◽  
Vol 06 (05) ◽  
pp. 623-634 ◽  
Author(s):  
WENXUE HUANG
Keyword(s):  
Lie Algebra ◽  
Jacobson Radical ◽  
Borel Subgroup ◽  
Unit Group ◽  
Zariski Closure ◽  
Closed Field ◽  
Associative Algebras ◽  
Lie Bracket ◽  
Algebraic Monoid ◽  
Relationship Of

Let A be a linear associative K-algebra with unity (LAA), K an algebraically closed field. A K–subalgebra of A containing the unity of A is referred to as a sub-LAA of A. A with respect to the multiplication (respectively, Lie bracket) is an algebraic monoid (respectively, Lie algebra) over K, denoted by AM (respectively, AL). Let G(A) and J(A) denote the unit group of AM and Jacobson radical of A, respectively. The following are proved in this paper. (i) If BM is a Borel submonoid of AM, the Zariski closure of a Borel subgroup of G(A), then B is a sub-LAA of A and [Formula: see text], where [Formula: see text] is the set of Borel submonoids of AM. (ii) If dim A≠3, then G(A) is nilpotent iff for every proper sub-LAA N of A, G(N) is nilpotent. In addition, a relationship of Borel submonoids of AM and Borel subalgebras of AL is revealed.

Early changes of lung function and structure in an elastase model of emphysema—a hyperpolarized 3He MRI study

2008 ◽  
Vol 104 (3) ◽  
pp. 773-786 ◽  
Author(s):  
Kiarash Emami ◽  
Robert V. Cadman ◽  
John M. Woodburn ◽  
Martin C. Fischer ◽  
Stephen J. Kadlecek ◽  
...  
Keyword(s):  
Lung Function ◽  
Lung Ventilation ◽  
Unit Group ◽  
Sprague Dawley ◽  
Sprague Dawley Rats ◽  
Entire Lung ◽  
Residual Capacity ◽  
Regional Basis ◽  
Mean Linear Intercept ◽  
Mri Study

Early changes of lung function and structure were studied in the presence of an elastase-induced model of emphysema in 35 Sprague-Dawley rats at mild (5 U/100 g) and moderate (10 U/100 g) severities. Lung ventilation was measured on a regional basis (at a planar resolution of 3.2 mm) by hyperpolarized 3He MRI at 5 and 10 wk after model induction. Subsequent to imaging, average alveolar diameter was measured from histological slices taken from the centers of each lobe. Changes of mean fractional ventilation, mean linear intercept, and intrasubject heterogeneity of ventilation were studied during disease progression. Mean fractional ventilation was significantly different between healthy controls (0.23 ± 0.04) and emphysematous animals at both time points in the 10-unit group (0.06 ± 0.02 and 0.12 ± 0.05, respectively). Changes in average alveolar diameter were not statistically observable until the 10th wk between healthy (37 ± 10 μm) and emphysematous rats (73 ± 25 and 95 ± 31 μm, for 5 and 10 units, respectively). Assessment of function-structure correlation suggested that the majority of the decline in fractional ventilation occurred in the first 5 wk, while enlargement of alveolar diameters appeared primarily between the 5th and 10th wk. A thresholding metric, based on the 20th percentile of fractional ventilation over the entire lung, was utilized to detect the onset of the disease with confidence, independent of whether the regional ventilation measurements were normalized with respect to the delivered tidal volume and estimated functional residual capacity of each individual rat.

Splanchnic Hypoperfusion-Directed Therapies in Trauma: A Prospective, Randomized Trial

2005 ◽  
Vol 71 (3) ◽  
pp. 252-260 ◽  
Author(s):  
Stephen M. Cohn ◽  
Stephen M. Cohn ◽  
Orlando Kirton ◽  
Margaret Brown ◽  
S. Morad Hameed ◽  
...  
Keyword(s):  
Randomized Trial ◽  
Injury Severity ◽  
Ischemia Reperfusion ◽  
Unit Group ◽  
Severe Trauma ◽  
Prospective Randomized Trial ◽  
Gastric Tonometry ◽  
Trauma Patients ◽  
Splanchnic Perfusion ◽  
Splanchnic Hypoperfusion

Splanchnic hypoperfusion as reflected by gastric intramucosal acidosis has been recognized as an important determinant of outcome in shock. A comprehensive splanchnic hypoperfusion-ischemia reperfusion (IRP) protocol was evaluated against conventional shock management protocols in critical trauma patients. The study was a prospective randomized trial comparing three therapeutic approaches to hypoperfusion after severe trauma in 151 trauma patients admitted to the intensive care unit. Group 1 patients received hemodynamic support based on conventional indicators of hypoperfusion. In group 2, resuscitation was further guided by gastric tonometry-derived estimates of splanchnic hypoperfusion and included more invasive hemodynamic monitoring and additional administration of colloid or crystalloid solutions, or inotropic support. Group 3 patients additionally received therapies specifically aimed at optimizing splanchnic perfusion and minimizing oxidant-mediated damage from reperfusion. The three groups were similar based on age, Injury Severity Score, and Acute Physiology and Chronic Health Evaluation II Scores. There were no statistically significant differences in mortality rates, organ dysfunction, ventilator days, or length of stay between any of the interventions. Techniques of optimization of splanchnic perfusion and minimization of oxidant-mediated reperfusion injury evaluated in this study were not advantageous relative to standard resuscitation measures guided by conventional or tonometric measures of hypoperfusion in the therapy of occult and clinical shock in trauma patients.

scholarly journals Smooth representations of unit groups of split basic algebras over non-Archimedean local fields

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Carlos A. M. André ◽  
João Dias
Keyword(s):  
Local Field ◽  
Unit Group ◽  
Basic Algebra ◽  
Local Fields ◽  
Dimensional Representation ◽  
Smooth Representation ◽  
One Dimensional ◽  
Finite Dimensional

Abstract We consider smooth representations of the unit group G = A × G=\mathcal{A}^{\times} of a finite-dimensional split basic algebra 𝒜 over a non-Archimedean local field. In particular, we prove a version of Gutkin’s conjecture, namely, we prove that every irreducible smooth representation of 𝐺 is compactly induced by a one-dimensional representation of the unit group of some subalgebra of 𝒜. We also discuss admissibility and unitarisability of smooth representations of 𝐺.

Research in Different Categories of UK Universities

1997 ◽  
Vol 11 (5) ◽  
pp. 304-313
Author(s):  
W. O. George ◽  
A. N. Hill
Keyword(s):  
Weighted Average ◽  
Unit Group ◽  
Research Quality ◽  
Average Score ◽  
Social Sciences And Humanities ◽  
Peer Rating ◽  
Subject Areas ◽  
Broad Subject ◽  
The Impact

In this paper, the origins and characteristics of the 102 current UK universities are briefly traced and the outcomes of recent assessments of research quality are summarized for all universities and for the 69 subject units within which assessment was made. The quality of research in a subject unit, group of subject units or complete institution is measured by a weighted average score based on a peer rating of submitted subject units from each university and the numerical values obtained are described within the limitations of the methodology developed. The authors consider the scores in terms of the characteristics of each university and the broad subject areas, science, engineering, social sciences and humanities. They then discuss the industrial link with research in terms of recent government policy inputs, university research outcomes and the impact of market forces on universities from diminishing patterns of some income streams.

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