241:
302:
41:
272:
286:
282:
296:
277:
49:
25:
228:. This gives an equivalence between the monoidal category of complexes over
33:
260:
232:
with the monoidal category of comodules over the
Pareigis Hopf algebra.
48:
as a natural example of a Hopf algebra that is neither commutative nor
17:
244:
is the quotient of the
Pareigis Hopf algebra obtained by putting
117:
261:"A noncommutative noncocommutative Hopf algebra in "nature""
64:, the Pareigis algebra is generated by elements
8:
36:are essentially the same as complexes over
276:
45:
40:, in the sense that the corresponding
140:to its inverse and has order 4.
44:are isomorphic. It was introduced by
7:
88: = 0. The coproduct takes
14:
169:can be made into a comodule over
161:is a complex with differential
173:by letting the coproduct take
128:to 1. The antipode takes
1:
278:10.1016/0021-8693(81)90224-6
319:
259:Pareigis, Bodo (1981),
242:Sweedler's Hopf algebra
144:Relation to complexes
76:, with the relations
22:Pareigis Hopf algebra
215:is the component of
165:of degree –1, then
60:As an algebra over
42:monoidal categories
96:⊗1 + (1/
310:
289:
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318:
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309:
308:
307:
293:
292:
258:
255:
248: = 1.
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227:
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189:
160:
146:
58:
46:Pareigis (1981)
12:
11:
5:
316:
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271:(2): 356–374,
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156:
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13:
10:
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2:
315:
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303:Hopf algebras
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127:
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111:
107:
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99:
95:
91:
87:
84: =
83:
80: +
79:
75:
71:
67:
63:
55:
53:
51:
50:cocommutative
47:
43:
39:
35:
31:
28:over a field
27:
23:
19:
268:
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56:Construction
37:
29:
26:Hopf algebra
21:
15:
32:whose left
265:J. Algebra
253:References
116:, and the
124:to 0 and
34:comodules
297:Category
236:See also
206:, where
287:0623814
24:is the
18:algebra
285:
120:takes
118:counit
20:, the
177:to Σ
136:and
104:and
72:, 1/
273:doi
219:in
152:= ⊕
148:If
132:to
108:to
92:to
16:In
299::
283:MR
281:,
269:70
267:,
263:,
199:dm
190:+
134:xy
100:)⊗
82:yx
78:xy
52:.
275::
246:y
230:k
225:n
221:M
217:m
212:n
208:m
203:n
197:⊗
195:x
192:y
187:n
183:m
181:⊗
179:y
175:m
171:H
167:M
163:d
158:n
154:M
150:M
138:y
130:x
126:y
122:x
114:y
112:⊗
110:y
106:y
102:x
98:y
94:x
90:x
86:x
74:y
70:y
68:,
66:x
62:k
38:k
30:k
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