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Page 1065 of Mathematical Reviews Vol. 48, Issue 4 [page]

1974 Mathematical Reviews  
One consequence is that for an open set U of a complete variety X the property of being semi-affine depends only on a Zariski neighbourhood of the comple- ment.  ...  In § 3 it is shown that V is semi-affine if and only if I'( Y) is integral over ['(V) for all closed subvarieties Y. Also [(V) is shown to be finitely generated as a k-algebra when V is semi-affine.  ... 

Page 3150 of Mathematical Reviews Vol. , Issue 2002E [page]

2002 Mathematical Reviews  
Let g = g(A) be an affine Lie algebra of type A3, (/ > 1) and W be its Weyl group. Let A be the root system of g and {ay, a),...,a/} be a fundamental system for A.  ...  For J(V) this was shown in the previous work cited above. Then the authors use this result to give a criterion of irreducibility for a V-module.  ... 

Page 1332 of Mathematical Reviews Vol. , Issue 81D [page]

1981 Mathematical Reviews  
If f: XY is a semi-algebraic map between semi-algebraic subsets X, Y in R”, R” respectively, it is known that there exists a (dim Y — 1)-dimensional semi-algebraic subset Z of Y such that f is locally  ...  {For the entire collection see MR 80i:41004.} J. G. Timourian (Edmonton, Alta.) Hardt, Robert M. 81d:32012 Semi-algebraic local-triviality in semi-algebraic mappings. Amer. J.  ... 

Invariant Ideals and Matsushima's Criterion [article]

Ivan V. Arzhantsev
2005 arXiv   pre-print
This allows to obtain an elementary proof of Matsushima's criterion: a homogeneous space G/H is an affine variety if and only if H is reductive.  ...  Let G be a reductive algebraic group and H a closed subgroup of G. Explicit constructions of G-invariant ideals in the algebra K[G/H] are given.  ...  Hausen for useful discussions. In particular, Proposition 4.1 appears during such a discussion. Thanks are also due to D.A. Timashev for valuable remarks.  ... 
arXiv:math/0506430v1 fatcat:zzcqaxpeqja7db72qxmuchtj4e

On the complement of a nef and big divisor on an algebraic variety

Francesco Russo
1996 Mathematical proceedings of the Cambridge Philosophical Society (Print)  
As is known, for a semi-ample divisor D, R(X,D) is a finitely generated ^-algebra (see [21] or [9]), while this property is no longer true for arbitrary nef and big divisors (see [21] ).  ...  Then we show that, if D is a nef and big divisor, every divisor in \mD\ has semi-affine complement for every m ^ 1 if and only if Proj (R(X,D) ) is an algebraic variety over k.  ...  £) (/) = F(Xf) is a finitely generated ^-algebra; by Proposition 5 and Corollary 2, X f is semi-affine for every feR(X,^C) + and then r^ is a proper morphism.  ... 
doi:10.1017/s0305004100074983 fatcat:wfyriqokmnh47entfsm3u2gadq

Page 6481 of Mathematical Reviews Vol. , Issue 96k [page]

1996 Mathematical Reviews  
From the main theorem (Satz 2.1) a functional completeness criterion for Tg can also be derived.  ...  [The maximal classes of (),, €Q Pol, {a} for Q C E,, (a criterion for finite semiprimal algebras with only trivial subalgebras)| Rostock. Math. Kollog. No. 48 (1995), 27-46.  ... 

Page 6171 of Mathematical Reviews Vol. , Issue 2001I [page]

2001 Mathematical Reviews  
(English summary) [A criterion for recognizing algebraically constructible functions] J. Reine Angew. Math. 526 (2000), 61-88. Let V be a real algebraic set.  ...  constant on each element of a finite semi-algebraic partition of V).  ... 

On Some Problems in Non-Commutative Probability

J. J. Vishnu, S. Sarakrishnan, G. Lebiru, Vel Gerai
2021 figshare.com  
are introduced for it.  ...  We observe that if A is nonnegative, pseudo-pointwise admissible and affine thenΛ ∼ C π,y .  ... 
doi:10.6084/m9.figshare.14602638.v1 fatcat:qvd7xp3ypjfszpjdunssdoaeau

ON ALGEBRAIC VOLUME DENSITY PROPERTY

SH. KALIMAN, F. KUTZSCHEBAUCH
2016 Transformation groups  
A smooth affine algebraic variety X equipped with an algebraic volume form ω has the algebraic volume density property (AVDP) if the Lie algebra generated by complete algebraic vector fields of ω-divergence  ...  As an application of this method we establish AVDP for any homogeneous space X = G/R that admits a G-invariant algebraic volume form where G is a linear algebraic group and R is a closed reductive subgroup  ...  Acknowledgements: This research was started during a visit of the first author to the University of Bern and continued during a visit of the second author to the University of Miami, Coral Gables.  ... 
doi:10.1007/s00031-015-9360-7 fatcat:4zu4waxs45bupklurpclf2w6ay

On algebraic volume density property [article]

Shulim Kaliman, Frank Kutzschebauch
2014 arXiv   pre-print
A smooth affine algebraic variety X equipped with an algebraic volume form ω has the algebraic volume density property (AVDP) if the Lie algebra generated by completely integrable algebraic vector fields  ...  As an application of this method we establish AVDP for any homogeneous space X=G/R that admits a G-invariant algebraic volume form where G is a linear algebraic group and R is a closed reductive subgroup  ...  Acknowledgements: This research was started during a visit of the first author to the University of Bern and continued during a visit of the second author to the University of Miami, Coral Gables.  ... 
arXiv:1201.4769v2 fatcat:busvbfwxqregjjsfhksstskk5m

A Ganzstellensatz for semi-algebraic sets and a boundedness criterion for rational functions [article]

Noa Lavi
2014 arXiv   pre-print
We use this result to deduce a criterion for a rational function to be bounded on an open semi algebraic subset of some irreducible variety over a real closed field or over an ordered field which is dense  ...  Let 〈 K,ν〉 be a real closed valued field, and let S⊆ K^n be an open semi-algebraic set.  ...  A Ganzstellensatz for open semi-algebraic sets Let K be a real closed valued field, V some irreducible real affine variety over K, and L = K(V ).  ... 
arXiv:1101.2116v5 fatcat:icg7hacrmjekjnei75lshzw2zq

Page 906 of Mathematical Reviews Vol. 46, Issue 4 [page]

1973 Mathematical Reviews  
Under suitable separability assumptions, a regularity criterion of the type “A, is regular if and only if D,(A), is free over A,” is deduced for semi- analytic A.  ...  The localization of a semi-analytic k-algebra at a prime ideal p is shown to have universal finite K-derivation for a suitable field K>k.  ... 

Toroidal affine Nash groups [article]

Mahir Bilen Can
2016 arXiv   pre-print
A toroidal affine Nash group is the affine Nash group analogue of an anti-affine algebraic group.  ...  Nash group, and this H is toroidal. (2) If G is a connected affine Nash group, then there exist a largest toroidal affine Nash subgroup G and a largest connected, normal, almost linear affine Nash subgroup  ...  Next, we obtain a useful criterion for toroidalness via algebraization. Lemma 3.5. Let G be a connected affine Nash group and φ : G → G be an algebraization.  ... 
arXiv:1509.06687v3 fatcat:cktwi3tahfdutees7yoawlfquy

Open locally semi-algebraic maps

Niels Schwartz
1988 Journal of Pure and Applied Algebra  
This means that real spectra and algebraic properties of rings of sections of locally semi-algebraic spaces play a role.  ...  In semi-algebraic geometry examples of open morphisms occur naturally, for example coverings.  ...  We will prove a similar result on openness for semi-algebraic mappings. Let f: M+N be a morphism of affine semi-algebraic spaces.  ... 
doi:10.1016/0022-4049(88)90017-5 fatcat:eowcwojdg5e5tl4y7wmldwmenq

Anti-affine algebraic groups [article]

Michel Brion
2008 arXiv   pre-print
We say that an algebraic group G over a field is anti-affine if every regular function on G is constant.  ...  We obtain a classification of these groups, with applications to the structure of algebraic groups in positive characteristics, and to the construction of many counterexamples to Hilbert's fourteenth problem  ...  The preceding argument yields another criterion for affineness of a group scheme; namely, the existence of a faithful action on a variety having a fixed point.  ... 
arXiv:0710.5211v3 fatcat:vwohxrkrkzfq5hccmc3mohphme
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