Results 301 to 310 of about 14,992,722 (358)

On Instantiating the Algebraic Group Model from Falsifiable Assumptions

IACR Cryptology ePrint Archive, 2020
We provide a standard-model implementation (of a relaxation) of the algebraic group model (AGM, [Fuchsbauer, Kiltz, Loss, CRYPTO 2018]). Specifically, we show that every algorithm that uses our group is algebraic, and hence “must know” a representation ...
Thomas Agrikola, D. Hofheinz, Julia Kastner   +2 more
semanticscholar   +1 more source

ON GROUPING IN RELATIONAL ALGEBRA

International Journal of Foundations of Computer Science, 1999
The concept of grouping in relational algebra is well-known from its connection to aggregation. In this paper we generalize the grouping notion by defining a simultaneous grouping of more than one relation, and we discuss the application of operations on grouping elements other than just arithmetic aggregation.
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Algebraic Groups of Automorphisms of Nilpotent Groups and Lie Algebras

Journal of the London Mathematical Society, 1986
It is shown that every linear algebraic group over a field of characteristic zero arises as the group of automorphisms induced on the commutator quotient L/[L,L] of some nilpotent Lie algebra L. More precisely, let K be an algebraically closed field of characteristic zero and let k be a subfield of K.
Bryant, R. M., Groves, J. R. J.
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Cohomology of Lie Algebras and Algebraic Groups

American Journal of Mathematics, 1986
Let \({\mathcal G}\) be a simple, simply connected algebraic group defined and split over the finite field of p elements, let G be the points of \({\mathcal G}\) in an algebraically closed field k and \(G_ 1\) the scheme theoretic kernel of the Frobenius morphism from G to itself.
Friedlander, Eric M., Parshall, Brian J.
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Semilocal Group Algebras

Mathematical Notes, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Stable Groups and Algebraic Groups

Journal of the London Mathematical Society, 2000
Let \(G\) be a stable, saturated group, \(p\) be the strong type of an element of \(G\), and \(\langle p\rangle\) be the smallest type-definable (over \(\text{acl}(\emptyset)\)) subgroup of \(G\) containing \(p^G\). By \textit{L. Newelski}'s theorem [Notre Dame J. Formal Logic 32, No.
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Derivation Algebra in Noncommutative Group Algebras

Proceedings of the Steklov Institute of Mathematics, 2020
The paper udner review deals with the study, for a generally infinite non-commutative discrete group \(G\), of the derivation algebras in the group algebra of \(G\) in terms of characters on a groupoid associated with the group. Necessary conditions are obtained for a character to define a derivation.
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The Derived Picard Group is a Locally Algebraic Group

, 2000
Let A be a finite-dimensional algebra over an algebraically closed field K. The derived Picard group DPicK(A) is the group of two-sided tilting complexes over A modulo isomorphism.
Amnon Yekutieli
semanticscholar   +1 more source

Algebraic group actions on noncommutative spectra

, 2008
Let G be an affine algebraic group and let R be an associative algebra with a rational action of G by algebra automorphisms. We study the induced G-action on the set Spec R of all prime ideals of R, viewed as a topological space with the Jacobson–Zariski
M. Lorenz
semanticscholar   +1 more source

Homomorphisms of Lie Algebras of Algebraic Groups and Analytic Groups

Canadian Mathematical Bulletin, 1995
AbstractLet be a Lie algebra homomorphism from the Lie algebra of G to the Lie algebra of H in the following cases: (i) G and H are irreducible algebraic groups over an algebraically closed field of characteristic 0, or (ii) G and H are linear complex analytic groups.
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