Invariants of mixed representations of quivers I

2003/05/27 by Alexandr N. Zubkov, A. N. Zubkov, Zubkov, A. N.
Mathematics · #13A50 #14L24 #16R30 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT #msc:13A50 #msc:14L24 #msc:16R30

paper · pdf · doi:10.48550/arxiv.math/0305386

42 pages

arxiv created 2003/05/27 · openalex publication_date 2003/05/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a new concept of mixed representations of quivers that is a generalization of ordinary representations of quivers and orthogonal (symplectic) representations of symmetric quivers introduced recently by Derksen and Weyman. We describe the generating invariants of mixed representations of quivers (First Fundamental Theorem) and prove additional results that allow us to describe the defining relations between them in the second article.

Related

• Invariants of mixed representations of quivers II : defining relations and applications
• Identities for mixed representations of quiver are finitely based
• Locally semi-simple representations of quivers
• Semi-invariants of 2-representations of quivers
• Semi-invariants of Symmetric Quivers