"Path algebras of quivers"의 두 판 사이의 차이
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imported>Pythagoras0 |
Pythagoras0 (토론 | 기여) |
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| 1번째 줄: | 1번째 줄: | ||
==introduction== | ==introduction== | ||
* Q quiver | * Q quiver | ||
| − | * a path in Q is a sequence | + | * a path in Q is a sequence <math>(i|\alpha_1,\alpha_2,\cdots,\alpha_l|j)</math> such that <math>s(\alpha_i)=t(\alpha_{i-1})</math> for all <math>i = 2, \cdots, l</math> |
* the path algebra of kQ of Q is the k-algebra with basis the set of all paths in Q with multiplication in the basis given by concatenation of two paths | * the path algebra of kQ of Q is the k-algebra with basis the set of all paths in Q with multiplication in the basis given by concatenation of two paths | ||
* path algebra of a quiver | * path algebra of a quiver | ||
2020년 11월 13일 (금) 18:28 판
introduction
- Q quiver
- a path in Q is a sequence \((i|\alpha_1,\alpha_2,\cdots,\alpha_l|j)\) such that \(s(\alpha_i)=t(\alpha_{i-1})\) for all \(i = 2, \cdots, l\)
- the path algebra of kQ of Q is the k-algebra with basis the set of all paths in Q with multiplication in the basis given by concatenation of two paths
- path algebra of a quiver
- given a quiver Q, a path p is a sequence of arrows with some conditions
- path algebra : set of all k-linear combinations of all paths (including e_i's)
- p_1p_2 will correspond to a composition \(p_2\circ p_1\) of two maps (\(U\overset{P_2}{\rightarrow }V\overset{P_1}{\rightarrow }W\))