Index

(C•)α, 9

C•, 1, 7

Nd-graded

complex, 9

MinGen(in≺(a)), 13

Path(c, c ), 8

m(w), 12

acyclic matching, 2, 7

infinite, 9

algebra

associative, 29

Cohen-Macaulay, 43

differential graded, 18

exterior, 31, 33

Koszul, 17, 25

semigroup, 25

alphabet, 15

Anick resolution, 11, 14, 17, 21, 23

bimodule, 30

binomial, 25

Cartan complex, 26

cellular chain complex, 8, 36

chain complex, 1, 7

cellular, 8, 36

complete intersection, 18, 29, 32

complex

Nn-graded, 9

multigraded, 9

critical vertex, 8

CW-complex, 35

P -graded, 35

regular, 37

cycle

directed, 2, 7

deterministic finite automaton, 24

DFA, 24

differential, 7

differential graded algebra, 18

directed

cycle, 2, 7

edge, 1

path, 2

weighted graph, 1, 7

discrete Morse theory, 1, 2, 7

algebraic, 1, 2, 8

edge

weight, 1, 7

exterior algebra, 31, 33

f-vector, 36

free module, 7

fully attached, 14, 15, 23, 24, 30

Gr¨obner

basis, 11

infinite, 27

non.commutative, 21

quadratic, 17, 21, 25

reduced, 11, 18, 31

representation, 15, 21

graph

directed weighted, 7

Hilbert series, 25, 32

Hochschild complex, 29, 58

Hochschild homology, 29

ideal, 11

Borel fixed, 35, 37

complete intersection, 18

generic initial, 37, 40

initial, 11

monomial, 37

non-commutative lattice, 21

p-Borel fixed, 35, 54

principal Borel fixed, 37

principal Cohen-Macaulay p-Borel fixed,

49

principal p-Borel fixed, 41

two-sided, 21, 30

initial ideal, 11

Koszul algebra, 17, 25

Koszul complex, 26

language, 15, 17

regular, 25

73