252:
313:
52:
283:
297:
293:
307:
288:
60:
36:
239:. This gives an equivalence between the monoidal category of complexes over
44:
271:
243:
with the monoidal category of comodules over the
Pareigis Hopf algebra.
17:
59:
as a natural example of a Hopf algebra that is neither commutative nor
28:
255:
is the quotient of the
Pareigis Hopf algebra obtained by putting
128:
272:"A noncommutative noncocommutative Hopf algebra in "nature""
75:, the Pareigis algebra is generated by elements
8:
47:are essentially the same as complexes over
287:
56:
51:, in the sense that the corresponding
151:to its inverse and has order 4.
55:are isomorphic. It was introduced by
7:
99: = 0. The coproduct takes
25:
180:can be made into a comodule over
172:is a complex with differential
184:by letting the coproduct take
139:to 1. The antipode takes
1:
289:10.1016/0021-8693(81)90224-6
330:
270:Pareigis, Bodo (1981),
253:Sweedler's Hopf algebra
155:Relation to complexes
87:, with the relations
33:Pareigis Hopf algebra
226:is the component of
176:of degree –1, then
71:As an algebra over
53:monoidal categories
107:⊗1 + (1/
16:(Redirected from
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300:
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21:
329:
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304:
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259: = 1.
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69:
57:Pareigis (1981)
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15:
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282:(2): 356–374,
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314:Hopf algebras
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98:
95: =
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91: +
90:
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64:
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61:cocommutative
58:
54:
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39:over a field
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34:
30:
19:
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67:Construction
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40:
37:Hopf algebra
32:
26:
43:whose left
276:J. Algebra
264:References
127:, and the
135:to 0 and
45:comodules
308:Category
247:See also
217:, where
18:Pareigis
298:0623814
35:is the
29:algebra
296:
131:takes
129:counit
31:, the
188:to Σ
147:and
115:and
83:, 1/
284:doi
230:in
163:= ⊕
159:If
143:to
119:to
103:to
27:In
310::
294:MR
292:,
280:70
278:,
274:,
210:dm
201:+
145:xy
111:)⊗
93:yx
89:xy
63:.
286::
257:y
241:k
236:n
232:M
228:m
223:n
219:m
214:n
208:⊗
206:x
203:y
198:n
194:m
192:⊗
190:y
186:m
182:H
178:M
174:d
169:n
165:M
161:M
149:y
141:x
137:y
133:x
125:y
123:⊗
121:y
117:y
113:x
109:y
105:x
101:x
97:x
85:y
81:y
79:,
77:x
73:k
49:k
41:k
20:)
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