$E_8$, the most exceptional group

DOI10.1090/bull/1540zbMath1398.20062arXiv1605.01721OpenAlexW2346544369WikidataQ56387042 ScholiaQ56387042MaRDI QIDQ2822848

Skip Garibaldi

Publication date: 5 October 2016

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.01721

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Exceptional (super)algebras (17B25) Exceptional groups (20G41)

Related Items

Exceptional unification of families and forces ⋮ Invariant Bilinear Forms on W-Graph Representations and Linear Algebra Over Integral Domains ⋮ Saint Petersburg school of the theory of linear groups. I: Prehistory ⋮ Sculpting the standard model from low-scale gauge-Higgs-matter \(\mathrm{E}_8\) grand unification in ten dimensions ⋮ A class of continuous non-associative algebras arising from algebraic groups including ⋮ A positive formula for the Ehrhart-like polynomials from root system chip-firing

Cites Work

• Shells of twisted flag varieties and the Rost invariant
• Motivic construction of cohomological invariants
• Degree three cohomological invariants of semisimple groups
• Essential dimension of algebraic groups, including bad characteristic
• Degree three cohomological invariants of reductive groups
• Cohomological invariants of algebraic tori
• The Kneser-Tits conjecture for groups with Tits-index \textsf{E}\(_{8,2}^{66}\) over an arbitrary field.
• Open problems on central simple algebras.
• Formula for the Rost invariant
• Families of rationally simply connected varieties over surfaces and torsors for semisimple groups
• Automorphisms of classical Lie algebras
• Elementary abelian p-subgroups of algebraic groups
• Lower bounds for essential dimensions via orthogonal representations.
• A centennial: Wilhelm Killing and the exceptional groups
• A geometric construction of the exceptional Lie algebras \(F_4\) and \(E_8\)
• Vanishing of trace forms in low characteristics. Appendix by Alexander Premet.
• Oktaven, Ausnahmegruppen und Oktavengeometrie
• Basic representations of affine Lie algebras and dual resonance models
• 3-graded root systems and grids in Jordan triple systems
• Chevalley groups over function fields and automorphic forms
• Automorphismes et déformations des variétés de Borel
• Splitting fields for \(E_8\)-torsors
• On the exceptional series, and its descendants
• Emergence of the theory of Lie groups. An essay in the history of mathematics 1869--1926
• Essential dimension of algebraic groups and integral representations of Weyl groups
• Do it yourself: the structure constants for Lie algebras of types \(E_l\)
• The greatest mathematical paper of all time
• Triality, exceptional Lie algebras and Deligne dimension formulas.
• Homomorphisms of the alternating group \({\mathcal A}_5\) into reductive groups.
• The spin-spin correlation function in the two-dimensional Ising model in a magnetic field at \(T=T_{c}\)
• Remark on the Serre \((\text{mod }5)\)-invariant for groups of type \(E_ 8\)
• Galois cohomology of the classical groups over fields of cohomological dimension \(\leq 2\)
• Groups over \(\mathbb{Z}\)
• Examples for embeddings of groups \(\text{PSL}_ 2(F_ p)\) into simple Lie groups
• There is no ``Theory of everything inside \(\text E_{8}\)
• The sphere packing problem in dimension 8
• Essential dimension: a survey
• The Lie algebras with a nondegenerate trace form
• The slice method for \(G\)-torsors
• Motives with exceptional Galois groups and the inverse Galois problem
• Groups of outer type \(E_{6}\) with trivial Tits algebras
• Groupes reductifs
• Über die Galoiskohomologie halbeinfacher Matrizengruppen. I
• Über die Galoiskohomologie halbeinfacher Matrizengruppen II
• Proof of global stability, transitional dynamics, and international capital flows in a two-country model of innovation and growth
• Problems of classifying associative or Lie algebras and triples of symmetric or skew-symmetric matrices are wild
• The torsion index of \(E_8\) and other groups
• The torsion index of the spin groups
• Les sous-groupes fermes de rang maximum des groupes de Lie clos
• Automorphisms of Albert algebras and a conjecture of Tits and Weiss
• Essential dimension of Albert algebras
• Rational rigidity for
• SIMPLE GROUPS STABILIZING POLYNOMIALS
• Descent in Buildings
• Serre’s Conjecture II: A Survey
• On the Kernel of the Rost Invariant for E 8 Modulo 3
• Degree 5 Invariant of E8
• Did a 1-dimensional magnet detect a 248-dimensional Lie algebra?
• Algebraic groups with few subgroups
• Restricting the Rost invariant to the center
• The octic E8 invariant
• The algebra of grand unified theories
• $J$-invariant of linear algebraic groups
• Cohomological invariants: exceptional groups and spin groups
• Jordan gradings on exceptional simple Lie algebras
• Trace Forms on Lie Algebras
• Models of isotropic simple lie algebras
• Spinor Construction of Vertex Operator Algebras, Triality, and 𝐸⁽¹⁾₈
• Exceptional Lie Algebras and Related Algebraic and Geometric Structures
• THE WEYL GROUP OF A GRADED LIE ALGEBRA
• Finite simple groups which projectively embed in an exceptional Lie group are classified!
• Minimal representations of E6, E7, and E8 and the generalized Capelli identity.
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Essential Dimensions of Algebraic Groups and a Resolution Theorem for G-Varieties
• The octonions
• Algèbres simples centrales de degré 5 et E₈
• On conjugacy classes in the Lie group E_8
• THE GROUP $ K_3$ FOR A FIELD
• A new construction of Moufang quadrangles of type 𝐸₆,𝐸₇ and 𝐸₈
• On the construction of semisimple Lie algebras and Chevalley groups
• WHAT IS...Essential Dimension?
• Some Forms of Exceptional Lie Algebras
• Finite-Dimensional Division Algebras over Fields
• The Exceptional Simple Lie Algebras F ₄ and E ₆
• Orthogonal involution on algebras of degree 16 and the Killing form of E8
• On the structure of parabolic subgroups
• Linear algebraic groups.
• Conformal and quasiconformal realizations of exceptional Lie groups
• The Rost invariant has trivial kernel for quasi-split groups of low rank
• Experimental evidence for the occurrence of \(E_8\) in nature and the radii of the Gosset circles.