Locally $$\mathbb {C}$$ C -Nash groups
作者: Elías BaroJuan VicenteMargarita Otero
作者单位: 1Departamento de Álgebra, Facultad de Matemáticas, Universidad Complutense de Madrid
2Departamento de Matemáticas, Universidad Autónoma de Madrid
刊名: Revista Matemática Complutense, 2019, Vol.32 (2), pp.531-558
来源数据库: Springer Nature Journal
DOI: 10.1007/s13163-018-0278-1
关键词: Semialgebraic setNash mapLocally $$\mathbb {C}$$ C -NashAlgebraic group
英文摘要: Abstract(#br)We introduce the category of locally $${\mathbb {C}}$$ C -Nash groups, basic examples of such groups are complex algebraic groups. We prove that the latter form a full subcategory. We also show that both, abelian locally Nash and abelian locally $${\mathbb {C}}$$ C -Nash groups, can be characterised via meromorphic maps admitting an algebraic addition theorem; we give an invariant of such groups associated to the groups of periods of a chart at the identity. Finally, we prove that the category of simply connected abelian locally $${\mathbb {C}}$$ C -Nash groups coincides with that of universal coverings of the abelian complex irreducible algebraic groups (a complex version of a result of Hrushovski and Pillay in Isr J Math 85(1–3):203–262, 1994 ; Conflu Math 3(4):577–585,...
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影响因子:0.377 (2012)

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