### Abstract

The index of a Lie algebra r is defined as min _{w∈r*}dim r_{w}, where r_{w} is the stabilizer of w under the coadjoint action of r on r^{*}. In this paper we derive simple formulas for the index of parabolic subalgebras of the even orthogonal algebra g=so(2n,k). We use these formulas to prove the conjecture that indq<n for any parabolic subalgebra or seaweed subalgebra (intersection of two weakly opposite parabolics) q of so(2n,k). Some partial results for subalgebras of g=so(2n+1,k) are also obtained.

Original language | English (US) |
---|---|

Pages (from-to) | 127-142 |

Number of pages | 16 |

Journal | Linear Algebra and Its Applications |

Volume | 374 |

DOIs | |

State | Published - Nov 15 2003 |

### Fingerprint

### Keywords

- Frobenius Lie algebra
- Lie algebra index
- Parabolic subalgebras
- Seaweed subalgebras

### ASJC Scopus subject areas

- Algebra and Number Theory
- Numerical Analysis

### Cite this

**Index of parabolic and seaweed subalgebras of so _{n} .** / Dvorsky, Alexander.

Research output: Contribution to journal › Article

_{n}',

*Linear Algebra and Its Applications*, vol. 374, pp. 127-142. https://doi.org/10.1016/S0024-3795(03)00552-4

}

TY - JOUR

T1 - Index of parabolic and seaweed subalgebras of son

AU - Dvorsky, Alexander

PY - 2003/11/15

Y1 - 2003/11/15

N2 - The index of a Lie algebra r is defined as min w∈r*dim rw, where rw is the stabilizer of w under the coadjoint action of r on r*. In this paper we derive simple formulas for the index of parabolic subalgebras of the even orthogonal algebra g=so(2n,k). We use these formulas to prove the conjecture that indq

AB - The index of a Lie algebra r is defined as min w∈r*dim rw, where rw is the stabilizer of w under the coadjoint action of r on r*. In this paper we derive simple formulas for the index of parabolic subalgebras of the even orthogonal algebra g=so(2n,k). We use these formulas to prove the conjecture that indq

KW - Frobenius Lie algebra

KW - Lie algebra index

KW - Parabolic subalgebras

KW - Seaweed subalgebras

UR - http://www.scopus.com/inward/record.url?scp=0141843654&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0141843654&partnerID=8YFLogxK

U2 - 10.1016/S0024-3795(03)00552-4

DO - 10.1016/S0024-3795(03)00552-4

M3 - Article

VL - 374

SP - 127

EP - 142

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -