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Title: Multiplicative invariant lattices in obtained by twisting of group algebras and some explicit characterizations
Authors: Albuquerque, Helena 
Kraußhar, Rolf Sören 
Keywords: Twisted group algebras; Lattices; Algebraic number fields; Generalized norm and trace functions
Issue Date: 2008
Citation: Journal of Algebra. 319:3 (2008) 1116-1131
Abstract: Let G be a finite group and be its group algebra defined over . If we define in G a 2-cochain F, then we can consider the algebra which is obtained from deforming the product, x.Fy=F(x,y)xy, [for all]x,y[set membership, variant]G. Examples of algebras are Clifford algebras and Cayley algebras like octonions. In this paper we consider generalizations of lattices with complex multiplication in the context of these twisted group algebras. We explain how these induce the natural algebraic structure to endow any arbitrary finite-dimensional lattice whose real components stem from any finite algebraic field extension over with a multiplicative closed structure. Furthermore, we develop some fully explicit characterizations in terms of generalized trace and norm functions.
Rights: openAccess
Appears in Collections:FCTUC Matemática - Artigos em Revistas Internacionais

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