Picard Groups of Algebraic Groups and an Affineness Criterion by Rosengarten, Zev

“…We prove that an algebraic group over a field $k$ is affine precisely when its Picard group is torsion, and show that in this case the Picard group is finite when $k$ is perfect, and the product of a finite group of order prime to $p$ and a $p$-primary group of finite exponent when $k$ is imperfect of characteristic $p$.…”
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Generic stabilizers for simple algebraic groups acting on orthogonal and symplectic Grassmannians by Aluna Rizzoli

“…We consider faithful actions of simple algebraic groups on self-dual irreducible modules and on the associated varieties of totally singular subspaces, under the assumption that the dimension of the group is at least as large as the dimension of the variety. …”
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Infinite volume and atoms at the bottom of the spectrum by Edwards, Sam, Fraczyk, Mikolaj, Lee, Minju, Oh, Hee

“…Let $G$ be a higher rank simple real algebraic group, or more generally, any semisimple real algebraic group with no rank one factors and $X$ the associated Riemannian symmetric space. …”
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Improved 2D Discrete Hyperchaos Mapping with Complex Behaviour and Algebraic Structure for Strong S-Boxes Generation by Musheer Ahmad, Eesa Al-Solami

“…This paper proposes to present a novel method of generating cryptographic dynamic substitution-boxes, which makes use of the combined effect of discrete hyperchaos mapping and algebraic group theory. Firstly, an improved 2D hyperchaotic map is proposed, which consists of better dynamical behaviour in terms of large Lyapunov exponents, excellent bifurcation, phase attractor, high entropy, and unpredictability. …”
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On equivariant bundles and their moduli spaces by Damiolini, Chiara

“…Let $G$ be an algebraic group and $\Gamma $ a finite subgroup of automorphisms of $G$. …”
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Groupes de Brauer algébriques modulo les constantes d’espaces homogènes et leurs compactifications by Linh, Nguyen Manh

“…We show that this inclusion is not always an isomorphism, even in the case where $X$ is a homogeneous space of a connected linear algebraic group over $K$. A similar result for the smooth compactifications of $X$ is also given.…”
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Uniform boundedness of $ (SL_2(\mathbb{C}))^{n} $ and $ (PSL_2(\mathbb{C}))^{n} $ by Fawaz Aseeri

“…Motivated by previously known results approximating $ \Delta(G) $ for any algebraic group $ G, $ we find the exact values of the conjugacy diameters of the direct product of finitely many copies of $ SL_2(\mathbb{C}) $ and the direct product of finitely many copies of $ PSL_2(\mathbb{C}). $ We also prove that if $ G_1, \dots, G_n $ be quasisimple groups such that $ G_i $ is uniformly bounded for each $ i\in \{1, \dots, n\}, $ then $ G_1\times\dots \times G_n $ is uniformly bounded. …”
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On linear algebraic semigroups III by Mohan S. Putcha

“…Using some results on linear algebraic groups, we show that every connected linear algebraic semigroup S contains a closed, connected diagonalizable subsemigroup T with zero such that E(T) intersects each regular J-class of S. …”
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Group-Valued Multisets by Andrei Alexandru, Gabriel Ciobanu

“…After presenting the algebraic groups in the framework of finitely supported sets, we study the finitely supported group-valued multisets. …”
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