Simple graded division algebras over the field of real numbers

DOI10.1016/j.laa.2015.10.021zbMath1395.16046arXiv1506.00281OpenAlexW2963144637MaRDI QIDQ898792

Mikhail V. Zaicev, Yu. A. Bakhturin

Publication date: 18 December 2015

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.00281

zbMATH Keywords

simple Lie algebragraded algebragradingfunctional identityprimitive algebra

Mathematics Subject Classification ID

Graded rings and modules (associative rings and algebras) (16W50) Finite-dimensional division rings (16K20)

Related Items (16)

Fine gradings and automorphism groups on associative algebras ⋮ Gradings on classical central simple real Lie algebras ⋮ Unnamed Item ⋮ Clifford algebras as twisted group algebras and the Arf invariant ⋮ Identities and central polynomials for real graded division algebras ⋮ Classification of division gradings on finite-dimensional simple real algebras. ⋮ Graded identities of simple real graded division algebras ⋮ Real representations of \(C_2\)-graded groups: the antilinear theory ⋮ Classification of involutions on graded-division simple real algebras ⋮ Gradings on associative algebras with involution and real forms of classical simple Lie algebras ⋮ Pauli gradings on Lie superalgebras and graded codimension growth ⋮ Graded division algebras over the field of real numbers ⋮ Graded-division algebras and Galois extensions ⋮ Graded-division algebras over arbitrary fields ⋮ On nonassociative graded-simple algebras over the field of real numbers ⋮ On generic \(G\)-graded Azumaya algebras

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Gradings on simple algebras of finitary matrices.
• Classification of group gradings on simple Lie algebras of types \(\mathcal A\), \(\mathcal B\), \(\mathcal C\) and \(\mathcal D\)
• Methods of graded rings.
• Gradings on simple Jordan and Lie algebras
• Lie gradings on associative algebras
• GROUP GRADINGS ON FINITARY SIMPLE LIE ALGEBRAS
• Group Gradings on Matrix Algebras

This page was built for publication: Simple graded division algebras over the field of real numbers