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Page 1065 of Mathematical Reviews Vol. 48, Issue 4
[page]
1974
Mathematical Reviews
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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
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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
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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]
2005
arXiv
pre-print
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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
1996
Mathematical proceedings of the Cambridge Philosophical Society (Print)
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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
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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
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(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
2021
figshare.com
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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
2016
Transformation groups
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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]
2014
arXiv
pre-print
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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]
2014
arXiv
pre-print
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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
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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]
2016
arXiv
pre-print
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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
1988
Journal of Pure and Applied Algebra
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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]
2008
arXiv
pre-print
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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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