ar X iv : 1 31 2 . 46 85 v 1 [ m at h . R A ] 1 7 D ec 2 01 3 EVOLUTION ALGEBRAS AND GRAPHS
نویسنده
چکیده
A digraph is attached to any evolution algebra. This graph leads to some new purely algebraic results on this class of algebras and allows for some new natural proofs of known results. Nilpotency of an evolution algebra will be proved to be equivalent to the nonexistence of oriented cycles in the graph. Besides, the automorphism group of any evolution algebra E with E = E will be shown to be always finite.
منابع مشابه
ar X iv : m at h / 03 10 31 4 v 2 [ m at h . R T ] 1 6 N ov 2 00 3 GEOMETRIC AND COMBINATORIAL REALIZATIONS OF CRYSTAL GRAPHS
For irreducible integrable highest weight modules of the finite and affine Lie algebras of type A and D, we define an isomorphism between the geometric realization of the crystal graphs in terms of irreducible components of Nakajima quiver varieties and the combinatorial realizations in terms of Young tableaux and Young walls. For type A (1) n , we extend the Young wall construction to arbitrar...
متن کاملar X iv : m at h / 03 10 31 4 v 3 [ m at h . R T ] 1 9 A ug 2 00 4 GEOMETRIC AND COMBINATORIAL REALIZATIONS OF CRYSTAL GRAPHS
For irreducible integrable highest weight modules of the finite and affine Lie algebras of type A and D, we define an isomorphism between the geometric realization of the crystal graphs in terms of irreducible components of Nakajima quiver varieties and the combinatorial realizations in terms of Young tableaux and Young walls. For type A (1) n , we extend the Young wall construction to arbitrar...
متن کاملar X iv : 0 71 2 . 16 20 v 1 [ m at h . R T ] 1 1 D ec 2 00 7 James ’ Conjecture for Hecke algebras of exceptional type , I
In this paper, and a second part to follow, we complete the programme (initiated more than 15 years ago) of determining the decomposition numbers and verifying James’ Conjecture for Iwahori–Hecke algebras of exceptional type. The new ingredients which allow us to achieve this aim are: • the fact, recently proved by the first author, that all Hecke algebras of finite type are cellular in the sen...
متن کاملar X iv : 0 90 3 . 13 81 v 1 [ m at h . C O ] 8 M ar 2 00 9 COMBINATORIAL HOPF ALGEBRAS AND TOWERS OF ALGEBRAS – DIMENSION , QUANTIZATION , AND FUNCTORIALITY
Bergeron and Li have introduced a set of axioms which guarantee that the Grothendieck groups of a tower of algebras L n≥0 An can be endowed with the structure of graded dual Hopf algebras. Hivert and Nzeutzhap, and independently Lam and Shimozono constructed dual graded graphs from primitive elements in Hopf algebras. In this paper we apply the composition of these constructions to towers of al...
متن کامل1 Koszul Algebras
The algebras Qn describe the relationship between the roots and coefficients of a non-commutative polynomial. I.Gelfand, S.Gelfand, and V. Retakh have defined quotients of these algebras corresponding to graphs. In this work we find the Hilbert series of the class of algebras corresponding to the n-vertex path, Pn. We also show this algebra is Koszul. We do this by first looking at class of qua...
متن کامل