The indecomposability of a certain bimodule given by the Brauer construction

Broué’s abelian defect conjecture [3, 6.2] predicts for a p-block of a finite group G with an abelian defect group P a derived equivalence between the block algebra and its Brauer correspondent. By a result of Rickard [11], such a derived equivalence would in particular imply a stable equivalence induced by tensoring with a suitable bimodule - and it appears that these stable equivalences in turn tend to be obtained by “gluing” together Morita equivalences at the local levels of the considered blocks; see e.g. [4, 6.3], [8, 3.1], [12, 4.1], and [13, 5.6, A.4.1]. This note provides a technical indecomposability result which is intended to verify in suitable circumstances the hypotheses that are necessary to apply gluing results as mentioned above. This is used in [7] to show that Broué’s abelian defect group conjecture holds for nonprincipal blocks of the simple Held group and the sporadic Suzuki group

Challenges of capturing engagement on Facebook for Altmetrics

Previous research shows that, despite its popularity, Facebook is less frequently used to share academic content. In order to investigate this discrepancy we set out to explore engagement numbers through their Graph API by querying the Facebook API with multiple URLs for a random set of 103,539 articles from the Web of Science. We identified two major challenge areas: mapping articles to URLs and the mapping URLs to objects inside Facebook. We then explored three problem cases within our dataset: (1) identifying a landing page for any given URL, (2) instances where equivalent URLs are mapped to different Facebook objects, and (3) instances of different articles being mapped onto the same Facebook object. We found that the engagement numbers for 11.8% of all articles that have been shared on Facebook at least once are not reliable because of these problems. Moreover, we were unable to identify the URL for 11.6% of the articles in our data. Taken together, the three problem cases constitute 12.3% of the 103,539 tested articles for which engagement numbers cannot be relied upon. Given that we only tested a small number of problem cases and URL variants, our results point to large challenges facing those wishing to collect Facebook metrics programatically through the available API.Comment: To be presented at the 23rd International Conference on Science and Technology Indicators (STI 2018