منابع مشابه
Classification of arithmetic root systems
Arithmetic root systems are invariants of Nichols algebras of diagonal type with a certain finiteness property. They can also be considered as generalizations of ordinary root systems with rich structure and many new examples. On the other hand, Nichols algebras are fundamental objects in the construction of quantized enveloping algebras, in the noncommutative differential geometry of quantum g...
متن کاملThe classification of root systems
2 Root systems Definition. Let E ∼= R be a vector space with an inner product 〈·, ·〉. A subset R ⊂ E \ {0} is called root system, if R has the following properties: (R1) R is finite and spans E, (R2) if α ∈ R, then −α ∈ R and ±α are the only multiples of α in R, (R3) R is invariant under the reflection in the hyperplane orthogonal to any α ∈ R (see Fig. 1), i.e., for all α, β ∈ R: sα(β) = β − 2...
متن کاملThe arithmetic Tutte polynomials of the classical root systems
Many combinatorial and topological invariants of a hyperplane arrangement can be computed in terms of its Tutte polynomial. Similarly, many invariants of a hypertoric arrangement can be computed in terms of its arithmetic Tutte polynomial. We compute the arithmetic Tutte polynomials of the classical root systems An, Bn, Cn, and Dn with respect to their integer, root, and weight lattices. We do ...
متن کاملThe Classification of Convex Orders on Affine Root Systems
We classify all total orders having a certain convexity property on the positive root system of an arbitrary untwisted affine Lie algebra g. Such total orders are called convex orders and were used to construct Poincaré-BirkhoffWitt type bases of the upper triangular subalgebra of the quantized enveloping algebra of g which are called convex bases.
متن کاملA Note on the First Geometric-Arithmetic Index of Hexagonal Systems and Phenylenes
The first geometric-arithmetic index was introduced in the chemical theory as the summation of 2 du dv /(du dv ) overall edges of the graph, where du stand for the degree of the vertex u. In this paper we give the expressions for computing the first geometric-arithmetic index of hexagonal systems and phenylenes and present new method for describing hexagonal system by corresponding a simple g...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2009
ISSN: 0001-8708
DOI: 10.1016/j.aim.2008.08.005