Special biserial algebras and right Gröbner bases
نویسندگان
چکیده
منابع مشابه
Multiplicative Bases, Gröbner Bases, and Right Gröbner Bases
Before surveying the results of the paper, we introduce path algebras. Path algebras play a central role in the representation theory of finite-dimensional algebras (Gabriel, 1980; Auslander et al., 1995; Bardzell, 1997) and the theory of Gröbner bases (Bergman, 1978; Mora, 1986; Farkas et al., 1993) has been an important tool in some results (Feustel et al., 1993; Green and Huang, 1995; Bardze...
متن کاملDerived equivalence of symmetric special biserial algebras
We introduce Brauer complex of symmetric SB-algebra, and reformulate in terms of Brauer complex the so far known invariants of stable and derived equivalence of symmetric SB-algebras. In particular, the genus of Brauer complex turns out to be invariant under derived equivalence. We study transformations of Brauer complexes which preserve class of derived equivalence. Additionally, we establish ...
متن کاملSpecial biserial algebras with no outer derivations
Let A be a special biserial algebra over an algebraically closed field. We show that the first Hohchshild cohomology group of A with coefficients in the bimodule A vanishes if and only if A is representation finite and simply connected (in the sense of Bongartz and Gabriel), if and only if the Euler characteristic of Q equals the number of indecomposable non uniserial projective injective A-mod...
متن کاملGröBner-Shirshov Bases and Embeddings of Algebras
In this paper, by using Gröbner-Shirshov bases, we show that in the following classes, each (resp. countably generated) algebra can be embedded into a simple (resp. two-generated) algebra: associative differential algebras, associative Ω-algebras, associative λ-differential algebras. We show that in the following classes, each countably generated algebra over a countable field k can be embedded...
متن کاملThe strong no loop conjecture for special biserial algebras
Let A be a finite dimensional algebra over a field given by a quiver with relations. Let S be a simple A-module with a non-split self-extension, that is, the quiver has a loop at the corresponding vertex. The strong no loop conjecture claims that S is of infinite projective dimension; see [1, 6]. This conjecture remains open except for monomial algebras; see, for example, [2, 6, 8, 11]. Under c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2003
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(03)00035-8