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Jul
2
awarded  Curious
Dec
9
comment Is every finitely dimensional basic $K$-algebra isomorphic to a bound quiver algebra?
Is every finite dimensional basic $K$-algebra connected?
Dec
9
comment Is every finitely dimensional basic $K$-algebra isomorphic to a bound quiver algebra?
Let $A$ be a basic and connected finite dimensional Kalgebra, then it is isomorphic to a bound quiver algebra by Theorem 3.7 p64, ( I. Assem, D. Simson and A. Skowro$\acute{n}$ski, Elements of the Representation Theory of Associative Algebras, Volume 1)
Dec
9
revised Is every finitely dimensional basic $K$-algebra isomorphic to a bound quiver algebra?
added 65 characters in body
Dec
9
revised Is every finitely dimensional basic $K$-algebra isomorphic to a bound quiver algebra?
added 161 characters in body; edited title
Dec
5
comment Is every finitely dimensional basic $K$-algebra isomorphic to a bound quiver algebra?
If a finite dimensional algebra $C$ with $C/radC\cong K$ and $rad^2C\cong radC\cong K$, then $C$ is two-dimensional.
Dec
3
comment Is every finitely dimensional basic $K$-algebra isomorphic to a bound quiver algebra?
Assume that $A$ is a $K$-algebra with a complete set ${e_1,\cdots , e_n}$ of primitive orthogonal idempotents. The algebra $A$ is called basic if $e_iA \ncong e_jA$, for all $i\neq j$.
Dec
1
awarded  Enthusiast
Nov
30
revised Is every finitely dimensional basic $K$-algebra isomorphic to a bound quiver algebra?
added 1489 characters in body
Nov
29
asked Is every finitely dimensional basic $K$-algebra isomorphic to a bound quiver algebra?
Nov
29
accepted Cartan or Coxeter matrix of an algebra of infinite global dimension
Nov
28
comment Cartan or Coxeter matrix of an algebra of infinite global dimension
Thank you very much, Aaron Is there a finite dimensional algebra $A$ satisfying the following conditions: (1) The Cartan matrix of $A$ is not invertible (2) $A$ has finite globle dimension.
Nov
22
revised Cartan or Coxeter matrix of an algebra of infinite global dimension
added 4 characters in body
Nov
21
asked Cartan or Coxeter matrix of an algebra of infinite global dimension
Nov
18
comment how to find all simple modules for the given path algebra
Thanks, Julian Kuelshammer. I learned sonething new from your answer. If the field is algebraically closed, does the path algebra $A=KQ$ above and the polynomial ring $R$ have infinitely dimensional simple representation?
Nov
16
revised how to find all simple modules for the given path algebra
added 44 characters in body; edited title
Nov
16
revised how to find all simple modules for the given path algebra
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Nov
16
asked how to find all simple modules for the given path algebra
Nov
15
awarded  Benefactor
Nov
15
accepted admissible ideals