TY - JOUR

T1 - Root graded groups revisited

AU - Воронецкий, Егор Юрьевич

PY - 2024/9/1

Y1 - 2024/9/1

N2 - A group G is called root graded if it has a family of subgroups Gα indexed by roots from a root system Φ satisfying natural conditions similar to Chevalley groups over commutative unital rings. For any such group there is a corresponding algebraic structure (commutative unital ring, associative unital ring, etc.) encoding the commutator relations between Gα. We give a complete description of varieties of such structures for irreducible root systems of rank ⩾3 excluding H3 and H4. Moreover, we provide a construction of root graded groups for all algebraic structures from these varieties.

AB - A group G is called root graded if it has a family of subgroups Gα indexed by roots from a root system Φ satisfying natural conditions similar to Chevalley groups over commutative unital rings. For any such group there is a corresponding algebraic structure (commutative unital ring, associative unital ring, etc.) encoding the commutator relations between Gα. We give a complete description of varieties of such structures for irreducible root systems of rank ⩾3 excluding H3 and H4. Moreover, we provide a construction of root graded groups for all algebraic structures from these varieties.

KW - 20E42

KW - Alternative rings

KW - Groups with commutator relations

KW - Root graded groups

UR - https://www.mendeley.com/catalogue/1fa11762-3b41-3f8b-a043-dded3f9bb151/

U2 - 10.1007/s40879-024-00760-2

DO - 10.1007/s40879-024-00760-2

M3 - Article

VL - 10

JO - European Journal of Mathematics

JF - European Journal of Mathematics

SN - 2199-675X

IS - 3

M1 - 50

ER -