Two-step solvable SKT shears

TY - JOUR

T1 - Two-step solvable SKT shears

AU - Freibert, Marco

AU - Swann, Andrew

N1 - Publisher Copyright: © 2021, The Author(s).

PY - 2021/12

Y1 - 2021/12

N2 - We use the shear construction to construct and classify a wide range of two-step solvable Lie groups admitting a left-invariant SKT structure. We reduce this to a specification of SKT shear data on Abelian Lie algebras, and which then is studied more deeply in different cases. We obtain classifications and structure results for g almost Abelian, for derived algebra g' of codimension 2 and not J-invariant, for g' totally real, and for g' of dimension at most 2. This leads to a large part of the full classification for two-step solvable SKT algebras of dimension six.

AB - We use the shear construction to construct and classify a wide range of two-step solvable Lie groups admitting a left-invariant SKT structure. We reduce this to a specification of SKT shear data on Abelian Lie algebras, and which then is studied more deeply in different cases. We obtain classifications and structure results for g almost Abelian, for derived algebra g' of codimension 2 and not J-invariant, for g' totally real, and for g' of dimension at most 2. This leads to a large part of the full classification for two-step solvable SKT algebras of dimension six.

U2 - 10.1007/s00209-021-02753-3

DO - 10.1007/s00209-021-02753-3

M3 - Journal article

AN - SCOPUS:85104866317

SN - 0025-5874

VL - 299

SP - 1703

EP - 1739

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3-4

ER -