## Homology, Homotopy and Applications

- Homology Homotopy Appl.
- Volume 4, Number 2 (2002), 227-258.

### Koszul homology and Lie algebras with application to generic forms and points

R. Fröberg and C. Löfwal

#### Abstract

We study the Koszul dual for general superalgebras, and apply it to the Koszul homology of a graded algebra. We show that a part of the Koszul homology algebra is related to the homotopy Lie algebra by means of Koszul duality. This is used to study the "Minimal Resolution Conjecture" and the "Ideal Generating Conjecture" for sets of generic points in projective space, and for quotients of the polynomial ring (or exterior algebra) modulo generic quadratic forms.

#### Article information

**Source**

Homology Homotopy Appl., Volume 4, Number 2 (2002), 227-258.

**Dates**

First available in Project Euclid: 13 February 2006

**Permanent link to this document**

https://projecteuclid.org/euclid.hha/1139852464

**Mathematical Reviews number (MathSciNet)**

MR1918511

**Zentralblatt MATH identifier**

1066.13014

**Subjects**

Primary: 13D25

Secondary: 13D02: Syzygies, resolutions, complexes 17B99: None of the above, but in this section

#### Citation

Fröberg, R.; Löfwal, C. Koszul homology and Lie algebras with application to generic forms and points. Homology Homotopy Appl. 4 (2002), no. 2, 227--258. https://projecteuclid.org/euclid.hha/1139852464