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Affine Algebraic Groups
We briefly recall some of the basic notions related to affine algebraic groups. If the reader is comfortable with reductive groups then this chapter...
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On some splitting properties for algebraic groups over algebraic extensions of global fields
We prove some new Hasse principles related with the property of being split or (strongly) quasi-split for connected smooth affine algebraic groups...
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FAITHFUL ACTIONS OF AUTOMORPHISM GROUPS OF FREE GROUPS ON ALGEBRAIC VARIETIES
Considering a certain construction of algebraic varieties X endowed with an algebraic action of the group Aut( F n ), n < ∞, we obtain a criterion for...
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Covering Numbers for Simple Algebraic Groups
Let G be a simple algebraic group over an algebraically closed field, and let C be a noncentral conjugacy class of G . The covering number c n ( G , C ) is...
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Counting intrinsic Diophantine approximations in simple algebraic groups
We establish an explicit asymptotic formula for the number of rational solutions of intrinsic Diophantine inequalities on simply-connected simple...
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Affine Algebraic Ricci Solitons Associated to the Yano Connections on Three-Dimensional Lorentzian Lie Groups
In this paper, we compute curvatures of Yano connections on three-dimensional Lorentzian Lie groups with some product structure. We define affine...
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Description of Coordinate Groups of Irreducible Algebraic Sets over Free 2-Nilpotent Groups
AbstractA convenient pure algebraic description of the coordinate groups of irreducible algebraic sets over a non-Abelian free 2-nilpotent group N ...
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On Morphisms Between Connected Commutative Algebraic Groups over a Field of Characteristic 0
Let K be a field of characteristic 0 and let G and H be connected commutative algebraic groups over K . Let Mor 0 ( G , H ) denote the set of morphisms of...
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Algebraic Foundations: Groups
Algebraic concepts such as groups, rings, and fields are essential for the study of symmetric key and public key cryptography.
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Upper bounds for eigenvalue multiplicities of almost cyclic elements in irreducible representations of simple algebraic groups
We study the rational irreducible representations of simple algebraic groups in which some non-central semisimple element has at most one eigenvalue...
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Covering Numbers of Unipotent Conjugacy Classes in Simple Algebraic Groups
For simple algebraic groups defined over algebraically closed fields of good characteristic, we give upper bounds on the covering numbers of...
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Kulakov Algebraic Systems on Groups
We define a Kulakov algebraic system as a three-sorted algebraic system satisfying the axioms of a physical structure. We prove a strong version of...
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On Algebraic-Geometric and Universal Theories of Abelian Groups
This paper is of an overview nature, accumulating results on algebraic geometry over Abelian groups and close to them model-theoretic results related...
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Canonical Connections and Algebraic Ricci Solitons of Three-dimensional Lorentzian Lie Groups
In this paper, the author computes canonical connections and Kobayashi-Nomizu connections and their curvature on three-dimensional Lorentzian Lie...
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The Inverse Galois Problem for Connected Algebraic Groups
We show that each connected group scheme of finite type over an arbitrary ground field is isomorphic to the component of the identity inside the...
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Algebraic realization for simple groups
Let G be a finite simple group with elementary abelian Sylow 2 subgroup. We show that every closed smooth G manifold has a strongly algebraic model.
