NONCOMMUTATIVE DUPLICATE AND VINBERG ALGEBRAS

2020 ◽  
Vol 48 (1) ◽  
pp. 19-36
Author(s):  
Alexis Tapsoba ◽  
Nakelgbamba Boukary Pilabré
Keyword(s):  
Vinberg Algebras

KV-COHOMOLOGY OF KOSZUL–VINBERG ALGEBROIDS AND POISSON MANIFOLDS

2005 ◽  
Vol 16 (09) ◽  
pp. 1033-1061 ◽  
Author(s):  
MICHEL NGUIFFO BOYOM
Keyword(s):  
Poisson Manifolds ◽  
Main Concern ◽  
Vinberg Algebras ◽  
Strong Relationships

The main concern of this paper is the study of the relationships between the KV-cohomology of Koszul–Vinberg algebras and some properties of various geometrical objects. In particular we show how the scalar KV-cohomology of real or holomorphic Koszul–Vinberg algebroids is closely related to real or holomorphic Poisson manifolds. In the appendix we point out strong relationships between the pioneer work of Nijenhuis [42] and the KV-cohomology.

COHOMOLOGY AND HOMOLOGY OF ABELIAN GROUPS GRADED KOSZUL–VINBERG ALGEBRAS

2009 ◽  
Vol 06 (02) ◽  
pp. 241-266 ◽  
Author(s):  
MICHEL NGUIFFO BOYOM ◽  
F. NGAKEU
Keyword(s):  
Abelian Groups ◽  
Graded Algebras ◽  
Graded Modules ◽  
Vinberg Algebras

We study abelian groups graded (or color) Koszul–Vinberg algebras and their modules. Koszul–Vinberg cohomology and homology of these algebras are studied. As applications, we investigate some extensions of graded algebras and graded modules.

scholarly journals The cohomology of Koszul–Vinberg algebras

2006 ◽  
Vol 225 (1) ◽  
pp. 119-153 ◽  
Author(s):  
Michel Nguiffo Boyom
Keyword(s):  
Vinberg Algebras

scholarly journals SPECIAL VINBERG CONES

2021 ◽  
Author(s):  
D. V. ALEKSEEVSKY ◽  
V. CORTÉS
Keyword(s):  
Vector Space ◽  
Convex Cone ◽  
Euclidean Jordan Algebra ◽  
Jordan Algebras ◽  
Euclidean Case ◽  
Euclidean Metric ◽  
Euclidean Vector Space ◽  
Lorentz Cone ◽  
Homogeneous Convex ◽  
Vinberg Algebras

AbstractThe paper is devoted to the generalization of the Vinberg theory of homogeneous convex cones. Such a cone is described as the set of “positive definite matrices” in the Vinberg commutative algebra ℋn of Hermitian T-matrices. These algebras are a generalization of Euclidean Jordan algebras and consist of n × n matrices A = (aij), where aii ∈ ℝ, the entry aij for i < j belongs to some Euclidean vector space (Vij ; 𝔤) and $$ {a}_{ji}={a}_{ij}^{\ast }=\mathfrak{g}\left({a}_{ij},\cdot \right)\in {V}_{ij}^{\ast } $$ a ji = a ij ∗ = g a ij ⋅ ∈ V ij ∗ belongs to the dual space $$ {V}_{ij}^{\ast }. $$ V ij ∗ . The multiplication of T-Hermitian matrices is defined by a system of “isometric” bilinear maps Vij × Vjk → Vij ; i < j < k, such that |aij ⋅ ajk| = |aij| ⋅ |aik|, alm ∈ Vlm. For n = 2, the Hermitian T-algebra ℋn= ℋ2 (V) is determined by a Euclidean vector space V and is isomorphic to a Euclidean Jordan algebra called the spin factor algebra and the associated homogeneous convex cone is the Lorentz cone of timelike future directed vectors in the Minkowski vector space ℝ1,1⊕ V . A special Vinberg Hermitian T-algebra is a rank 3 matrix algebra ℋ3(V; S) associated to a Clifford Cl(V )-module S together with an “admissible” Euclidean metric 𝔤S.We generalize the construction of rank 2 Vinberg algebras ℋ2(V ) and special Vinberg algebras ℋ3(V; S) to the pseudo-Euclidean case, when V is a pseudo-Euclidean vector space and S = S0 ⊕ S1 is a ℤ2-graded Clifford Cl(V )-module with an admissible pseudo-Euclidean metric. The associated cone 𝒱 is a homogeneous, but not convex cone in ℋm; m = 2; 3. We calculate the characteristic function of Koszul-Vinberg for this cone and write down the associated cubic polynomial. We extend Baez’ quantum-mechanical interpretation of the Vinberg cone 𝒱2 ⊂ ℋ2(V ) to the special rank 3 case.

Sign in / Sign up

Export Citation Format

Share Document